sage:E = EllipticCurve("hw1")
E.isogeny_class()
Elliptic curves in class 346560.hw
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
346560.hw1 |
346560hw2 |
[0,1,0,−69261,6992829] |
1590409933520896/45 |
1039680 |
[] |
559872 |
1.1151
|
|
346560.hw2 |
346560hw1 |
[0,1,0,−861,9189] |
3058794496/91125 |
2105352000 |
[] |
186624 |
0.56582
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 346560.hw have
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1−T |
5 | 1+T |
19 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
7 |
1−2T+7T2 |
1.7.ac
|
11 |
1−3T+11T2 |
1.11.ad
|
13 |
1+4T+13T2 |
1.13.e
|
17 |
1+17T2 |
1.17.a
|
23 |
1+6T+23T2 |
1.23.g
|
29 |
1−3T+29T2 |
1.29.ad
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 346560.hw 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.