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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 11424.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11424.s1 | 11424r2 | \([0, 1, 0, -1272, -17892]\) | \(444893916104/9639\) | \(4935168\) | \([2]\) | \(3584\) | \(0.40071\) | |
| 11424.s2 | 11424r3 | \([0, 1, 0, -337, 2015]\) | \(1036433728/122451\) | \(501559296\) | \([2]\) | \(3584\) | \(0.40071\) | |
| 11424.s3 | 11424r1 | \([0, 1, 0, -82, -280]\) | \(964430272/127449\) | \(8156736\) | \([2, 2]\) | \(1792\) | \(0.054141\) | \(\Gamma_0(N)\)-optimal |
| 11424.s4 | 11424r4 | \([0, 1, 0, 128, -1288]\) | \(449455096/1753941\) | \(-898017792\) | \([2]\) | \(3584\) | \(0.40071\) |
Rank
sage: E.rank()
The elliptic curves in class 11424.s have rank \(1\).
Complex multiplication
The elliptic curves in class 11424.s do not have complex multiplication.Modular form 11424.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
