E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7360.o
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
7360.o1 |
7360y3 |
[0,0,0,−1772,17136] |
18778674312/6996025 |
229245747200 |
[4] |
5632 |
0.87971
|
|
7360.o2 |
7360y2 |
[0,0,0,−772,−8064] |
12422690496/330625 |
1354240000 |
[2,2] |
2816 |
0.53313
|
|
7360.o3 |
7360y1 |
[0,0,0,−767,−8176] |
779704121664/575 |
36800 |
[2] |
1408 |
0.18656
|
Γ0(N)-optimal |
7360.o4 |
7360y4 |
[0,0,0,148,−26096] |
10941048/8984375 |
−294400000000 |
[2] |
5632 |
0.87971
|
|
The elliptic curves in class 7360.o have
rank 0.
The elliptic curves in class 7360.o 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.