E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 337896f
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
337896.f3 |
337896f1 |
[0,0,0,−23826,816221] |
2725888/1053 |
577826543251152 |
[2] |
884736 |
1.5315
|
Γ0(N)-optimal |
337896.f2 |
337896f2 |
[0,0,0,−170031,−26407150] |
61918288/1521 |
13354213444026624 |
[2,2] |
1769472 |
1.8781
|
|
337896.f4 |
337896f3 |
[0,0,0,24909,−83446594] |
48668/85683 |
−3009149429387332608 |
[2] |
3538944 |
2.2247
|
|
337896.f1 |
337896f4 |
[0,0,0,−2704251,−1711663450] |
62275269892/39 |
1369662917336064 |
[2] |
3538944 |
2.2247
|
|
The elliptic curves in class 337896f have
rank 2.
The elliptic curves in class 337896f do not have complex multiplication.
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.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.