sage:E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 77760.dm
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
77760.dm1 |
77760br2 |
[0,0,0,−700812,225813744] |
819699324507/80 |
3715041853440 |
[] |
497664 |
1.8450
|
|
77760.dm2 |
77760br1 |
[0,0,0,−9612,236784] |
1541767203/512000 |
32614907904000 |
[] |
165888 |
1.2957
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 77760.dm have
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1 |
5 | 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.d
|
13 |
1−4T+13T2 |
1.13.ae
|
17 |
1−3T+17T2 |
1.17.ad
|
19 |
1−4T+19T2 |
1.19.ae
|
23 |
1−6T+23T2 |
1.23.ag
|
29 |
1+29T2 |
1.29.a
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 77760.dm 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.
(1331)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.