E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 46410.bz
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
46410.bz1 |
46410ca4 |
[1,0,0,−73171,7584245] |
43325247696520145329/183535468285260 |
183535468285260 |
[2] |
270336 |
1.5912
|
|
46410.bz2 |
46410ca2 |
[1,0,0,−6871,−13735] |
35874636409222129/20685941312400 |
20685941312400 |
[2,2] |
135168 |
1.2446
|
|
46410.bz3 |
46410ca1 |
[1,0,0,−4871,−130935] |
12781554414694129/36385440000 |
36385440000 |
[2] |
67584 |
0.89802
|
Γ0(N)-optimal |
46410.bz4 |
46410ca3 |
[1,0,0,27429,−102915] |
2282194455855813071/1325495413520460 |
−1325495413520460 |
[2] |
270336 |
1.5912
|
|
The elliptic curves in class 46410.bz have
rank 1.
The elliptic curves in class 46410.bz 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 LMFDB numbering.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.