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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 77616cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.k2 | 77616cr1 | \([0, 0, 0, -44247, -3865610]\) | \(-1272112/121\) | \(-911245137884928\) | \([2]\) | \(516096\) | \(1.6122\) | \(\Gamma_0(N)\)-optimal |
| 77616.k1 | 77616cr2 | \([0, 0, 0, -723387, -236810630]\) | \(1389715708/11\) | \(331361868321792\) | \([2]\) | \(1032192\) | \(1.9587\) |
Rank
sage: E.rank()
The elliptic curves in class 77616cr have rank \(0\).
Complex multiplication
The elliptic curves in class 77616cr do not have complex multiplication.Modular form 77616.2.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.
