sage:E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 106560bh
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
106560.be2 |
106560bh1 |
[0,0,0,−6528,78752] |
2575826944/1266325 |
15124904755200 |
[] |
138240 |
1.2222
|
Γ0(N)-optimal |
106560.be1 |
106560bh2 |
[0,0,0,−432768,109579808] |
750484394082304/578125 |
6905088000000 |
[] |
414720 |
1.7715
|
|
sage:E.rank()
The elliptic curves in class 106560bh have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1 |
5 | 1+T |
37 | 1+T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
7 |
1+T+7T2 |
1.7.b
|
11 |
1−3T+11T2 |
1.11.ad
|
13 |
1+2T+13T2 |
1.13.c
|
17 |
1+3T+17T2 |
1.17.d
|
19 |
1+2T+19T2 |
1.19.c
|
23 |
1+23T2 |
1.23.a
|
29 |
1+3T+29T2 |
1.29.d
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 106560bh 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.
(1331)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.