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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 126960.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.s1 | 126960bb2 | \([0, -1, 0, -21117856, 75808358656]\) | \(-3247061909089/5859375000\) | \(-1879463646744000000000000\) | \([]\) | \(22892544\) | \(3.3479\) | |
| 126960.s2 | 126960bb1 | \([0, -1, 0, 2242784, -2178801920]\) | \(3889584671/8640000\) | \(-2771381914942832640000\) | \([]\) | \(7630848\) | \(2.7986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.s have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.s do not have complex multiplication.Modular form 126960.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
