sage:E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1058c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
1058.a2 |
1058c1 |
[1,0,1,0,2] |
23/4 |
−2116 |
[] |
80 |
−0.68263
|
Γ0(N)-optimal |
1058.a1 |
1058c2 |
[1,0,1,−115,462] |
−313994137/64 |
−33856 |
[] |
240 |
−0.13332
|
|
sage:E.rank()
The elliptic curves in class 1058c have
rank 2.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+T |
23 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
3 |
1+3T2 |
1.3.a
|
5 |
1+4T+5T2 |
1.5.e
|
7 |
1−4T+7T2 |
1.7.ae
|
11 |
1+2T+11T2 |
1.11.c
|
13 |
1+2T+13T2 |
1.13.c
|
17 |
1−2T+17T2 |
1.17.ac
|
19 |
1−2T+19T2 |
1.19.ac
|
29 |
1−2T+29T2 |
1.29.ac
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 1058c 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.