sage:E = EllipticCurve("jy1")
E.isogeny_class()
Elliptic curves in class 141120jy
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
141120.oq4 |
141120jy1 |
[0,0,0,65268,−10224144] |
1367631/2800 |
−62952607265587200 |
[2] |
1179648 |
1.9078
|
Γ0(N)-optimal |
141120.oq3 |
141120jy2 |
[0,0,0,−499212,−109798416] |
611960049/122500 |
2754176567869440000 |
[2,2] |
2359296 |
2.2544
|
|
141120.oq2 |
141120jy3 |
[0,0,0,−2474892,1400411376] |
74565301329/5468750 |
122954311065600000000 |
[2] |
4718592 |
2.6010
|
|
141120.oq1 |
141120jy4 |
[0,0,0,−7555212,−7992761616] |
2121328796049/120050 |
2699093036512051200 |
[2] |
4718592 |
2.6010
|
|
sage:E.rank()
The elliptic curves in class 141120jy have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1 |
5 | 1−T |
7 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
11 |
1+2T+11T2 |
1.11.c
|
13 |
1+6T+13T2 |
1.13.g
|
17 |
1+2T+17T2 |
1.17.c
|
19 |
1+4T+19T2 |
1.19.e
|
23 |
1+2T+23T2 |
1.23.c
|
29 |
1+29T2 |
1.29.a
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 141120jy do not have complex multiplication.
sage:E.q_eigenform(10)
sage:E.isogeny_class().matrix()
The i,j entry is the smallest degree of a cyclic isogeny between the i-th and j-th curve in the isogeny class, in the Cremona numbering.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.