E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 67760p
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
67760.bm4 |
67760p1 |
[0,0,0,−5687,407286] |
−44851536/132055 |
−59889532890880 |
[2] |
122880 |
1.3305
|
Γ0(N)-optimal |
67760.bm3 |
67760p2 |
[0,0,0,−124267,16842474] |
116986321764/148225 |
268891780326400 |
[2,2] |
245760 |
1.6771
|
|
67760.bm2 |
67760p3 |
[0,0,0,−158147,6929186] |
120564797922/64054375 |
232399324424960000 |
[2] |
491520 |
2.0237
|
|
67760.bm1 |
67760p4 |
[0,0,0,−1987667,1078607794] |
239369344910082/385 |
1396840417280 |
[2] |
491520 |
2.0237
|
|
The elliptic curves in class 67760p have
rank 0.
The elliptic curves in class 67760p 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.