E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6384c
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
6384.f4 |
6384c1 |
[0,−1,0,41,−86] |
464857088/410571 |
−6569136 |
[2] |
1024 |
−0.0043898
|
Γ0(N)-optimal |
6384.f3 |
6384c2 |
[0,−1,0,−204,−576] |
3685542352/1432809 |
366799104 |
[2,2] |
2048 |
0.34218
|
|
6384.f1 |
6384c3 |
[0,−1,0,−2864,−58032] |
2538016415428/872613 |
893555712 |
[2] |
4096 |
0.68876
|
|
6384.f2 |
6384c4 |
[0,−1,0,−1464,21600] |
339112345828/8210223 |
8407268352 |
[4] |
4096 |
0.68876
|
|
The elliptic curves in class 6384c have
rank 0.
The elliptic curves in class 6384c 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.