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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 126960cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.cm2 | 126960cs1 | \([0, 1, 0, -105976, -24061996]\) | \(-217081801/285660\) | \(-173211369683927040\) | \([2]\) | \(1824768\) | \(2.0007\) | \(\Gamma_0(N)\)-optimal |
| 126960.cm1 | 126960cs2 | \([0, 1, 0, -2052696, -1132135020]\) | \(1577505447721/838350\) | \(508337715376742400\) | \([2]\) | \(3649536\) | \(2.3472\) |
Rank
sage: E.rank()
The elliptic curves in class 126960cs have rank \(0\).
Complex multiplication
The elliptic curves in class 126960cs do not have complex multiplication.Modular form 126960.2.a.cs
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
