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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 342720cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 342720.cr2 | 342720cr1 | \([0, 0, 0, -969708, 961121968]\) | \(-527690404915129/1782829440000\) | \(-340704011684413440000\) | \([2]\) | \(11796480\) | \(2.6260\) | \(\Gamma_0(N)\)-optimal |
| 342720.cr1 | 342720cr2 | \([0, 0, 0, -21705708, 38874824368]\) | \(5918043195362419129/8515734343200\) | \(1627382175810925363200\) | \([2]\) | \(23592960\) | \(2.9725\) |
Rank
sage: E.rank()
The elliptic curves in class 342720cr have rank \(1\).
Complex multiplication
The elliptic curves in class 342720cr do not have complex multiplication.Modular form 342720.2.a.cr
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.
