sage:E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 221952.bi
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
221952.bi1 |
221952ba4 |
[0,1,0,−748317,−249407685] |
58591911104/243 |
192198386221056 |
[2] |
1638400 |
1.9502
|
|
221952.bi2 |
221952ba3 |
[0,1,0,−46047,−4034547] |
−873722816/59049 |
−729753247683072 |
[2] |
819200 |
1.6036
|
|
221952.bi3 |
221952ba2 |
[0,1,0,−8477,288315] |
85184/3 |
2372819582976 |
[2] |
327680 |
1.1455
|
|
221952.bi4 |
221952ba1 |
[0,1,0,193,16077] |
64/9 |
−111225917952 |
[2] |
163840 |
0.79889
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 221952.bi have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1−T |
17 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
5 |
1−2T+5T2 |
1.5.ac
|
7 |
1+2T+7T2 |
1.7.c
|
11 |
1+11T2 |
1.11.a
|
13 |
1+4T+13T2 |
1.13.e
|
19 |
1−4T+19T2 |
1.19.ae
|
23 |
1−4T+23T2 |
1.23.ae
|
29 |
1−6T+29T2 |
1.29.ag
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 221952.bi 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 LMFDB numbering.
⎝⎜⎜⎛12510211055101210521⎠⎟⎟⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.