sage:E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 107800i
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
107800.be4 |
107800i1 |
[0,0,0,−57575,−13119750] |
−44851536/132055 |
−62144554780000000 |
[2] |
589824 |
1.9093
|
Γ0(N)-optimal |
107800.be3 |
107800i2 |
[0,0,0,−1258075,−542540250] |
116986321764/148225 |
279016368400000000 |
[2,2] |
1179648 |
2.2558
|
|
107800.be2 |
107800i3 |
[0,0,0,−1601075,−223207250] |
120564797922/64054375 |
241149861260000000000 |
[2] |
2359296 |
2.6024
|
|
107800.be1 |
107800i4 |
[0,0,0,−20123075,−34744785250] |
239369344910082/385 |
1449435680000000 |
[2] |
2359296 |
2.6024
|
|
sage:E.rank()
The elliptic curves in class 107800i have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
5 | 1 |
7 | 1 |
11 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
3 |
1+2T+3T2 |
1.3.c
|
13 |
1+7T+13T2 |
1.13.h
|
17 |
1+7T+17T2 |
1.17.h
|
19 |
1−3T+19T2 |
1.19.ad
|
23 |
1+23T2 |
1.23.a
|
29 |
1−4T+29T2 |
1.29.ae
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 107800i 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.