One semester of elliptic curves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
2006
|
| Series: | EMS series of lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 130 S. Ill., graph. Darst. |
| ISBN: | 9783037190159 3037190159 |
Staff View
MARC
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| 100 | 1 | |a Ekedahl, Torsten |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a One semester of elliptic curves |c Torsten Ekedahl |
| 264 | 1 | |a Zürich |b European Mathematical Society |c 2006 | |
| 300 | |a VIII, 130 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS series of lectures in mathematics | |
| 650 | 4 | |a Courbes elliptiques | |
| 650 | 7 | |a Elliptische oppervlakken |2 gtt | |
| 650 | 4 | |a Fonctions elliptiques | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Elliptic functions | |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
v
1
Elliptic integrals
1
2
Elliptic curves
10
2.1
The shape of elliptic curves
....................... 12
2.2
Elliptic integrals revisited
........................ 18
3
Elliptic functions
24
3.1
Poles and zeroes
............................. 32
4
A projectíve
interlude
41
5
The group structure on an elliptic curve
47
6
Equivalence
52
6.1
Equivalences of elliptic curves
..................... 52
6.2
Equivalence of periods
......................... 54
6.3
The
j
-function
............................. 57
7
Formulaire
68
8
Finite fields
70
8.1
The curve y2
=
Xі
+ 1......................... 73
8.2
Normal forms and twists
........................ 75
9
Division polynomials
78
9.1
Algebraic version
............................ 82
10
Torsion points
88
11
Lattice inclusions
94
11.1
Complex multiplication
......................... 100
11.1.1
Complex multiplication lattices
................. 102
11.2
Elliptic curve interpretation
....................... 104
12
Modular forms
109
12.1
Elliptic curve interpretation
.......................
Ill
12.2
Modular forms of higher level
..................... 114
12.2.1
Sums of four squares
....................... 120
viii Contents
Hints to exercises
125
Solutions to exercises
127
Some further reading
128
Index
129
|
| adam_txt |
Contents
Preface
v
1
Elliptic integrals
1
2
Elliptic curves
10
2.1
The shape of elliptic curves
. 12
2.2
Elliptic integrals revisited
. 18
3
Elliptic functions
24
3.1
Poles and zeroes
. 32
4
A projectíve
interlude
41
5
The group structure on an elliptic curve
47
6
Equivalence
52
6.1
Equivalences of elliptic curves
. 52
6.2
Equivalence of periods
. 54
6.3
The
j
-function
. 57
7
Formulaire
68
8
Finite fields
70
8.1
The curve y2
=
Xі
+ 1. 73
8.2
Normal forms and twists
. 75
9
Division polynomials
78
9.1
Algebraic version
. 82
10
Torsion points
88
11
Lattice inclusions
94
11.1
Complex multiplication
. 100
11.1.1
Complex multiplication lattices
. 102
11.2
Elliptic curve interpretation
. 104
12
Modular forms
109
12.1
Elliptic curve interpretation
.
Ill
12.2
Modular forms of higher level
. 114
12.2.1
Sums of four squares
. 120
viii Contents
Hints to exercises
125
Solutions to exercises
127
Some further reading
128
Index
129 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:25:12Z |
| indexdate | 2024-07-09T20:37:56Z |
| institution | BVB |
| isbn | 9783037190159 3037190159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014746878 |
| oclc_num | 70139524 |
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| physical | VIII, 130 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | European Mathematical Society |
| record_format | marc |
| series2 | EMS series of lectures in mathematics |
| spelling | Ekedahl, Torsten Verfasser aut One semester of elliptic curves Torsten Ekedahl Zürich European Mathematical Society 2006 VIII, 130 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS series of lectures in mathematics Courbes elliptiques Elliptische oppervlakken gtt Fonctions elliptiques Curves, Elliptic Elliptic functions Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s DE-604 Erscheint auch als Ekedahl, Torsten One semester of elliptic curves Online-Ausgabe 978-3-03719-515-4 (DE-604)BV036705991 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014746878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ekedahl, Torsten One semester of elliptic curves Courbes elliptiques Elliptische oppervlakken gtt Fonctions elliptiques Curves, Elliptic Elliptic functions Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4014487-2 |
| title | One semester of elliptic curves |
| title_auth | One semester of elliptic curves |
| title_exact_search | One semester of elliptic curves |
| title_exact_search_txtP | One semester of elliptic curves |
| title_full | One semester of elliptic curves Torsten Ekedahl |
| title_fullStr | One semester of elliptic curves Torsten Ekedahl |
| title_full_unstemmed | One semester of elliptic curves Torsten Ekedahl |
| title_short | One semester of elliptic curves |
| title_sort | one semester of elliptic curves |
| topic | Courbes elliptiques Elliptische oppervlakken gtt Fonctions elliptiques Curves, Elliptic Elliptic functions Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Courbes elliptiques Elliptische oppervlakken Fonctions elliptiques Curves, Elliptic Elliptic functions Elliptische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014746878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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