E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5520.q
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
5520.q1 |
5520e3 |
[0,1,0,−2456,−47676] |
1600610497636/9315 |
9538560 |
[2] |
3584 |
0.52925
|
|
5520.q2 |
5520e2 |
[0,1,0,−156,−756] |
1650587344/119025 |
30470400 |
[2,2] |
1792 |
0.18267
|
|
5520.q3 |
5520e1 |
[0,1,0,−31,44] |
212629504/43125 |
690000 |
[2] |
896 |
−0.16390
|
Γ0(N)-optimal |
5520.q4 |
5520e4 |
[0,1,0,144,−3036] |
320251964/4197615 |
−4298357760 |
[2] |
3584 |
0.52925
|
|
The elliptic curves in class 5520.q have
rank 0.
The elliptic curves in class 5520.q 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.