E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1575.h
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
1575.h1 |
1575f3 |
[1,−1,0,−25317,1556716] |
157551496201/13125 |
149501953125 |
[2] |
3072 |
1.1881
|
|
1575.h2 |
1575f2 |
[1,−1,0,−1692,21091] |
47045881/11025 |
125581640625 |
[2,2] |
1536 |
0.84149
|
|
1575.h3 |
1575f1 |
[1,−1,0,−567,−4784] |
1771561/105 |
1196015625 |
[2] |
768 |
0.49492
|
Γ0(N)-optimal |
1575.h4 |
1575f4 |
[1,−1,0,3933,127966] |
590589719/972405 |
−11076300703125 |
[2] |
3072 |
1.1881
|
|
The elliptic curves in class 1575.h have
rank 0.
The elliptic curves in class 1575.h 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.