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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9744.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9744.r1 | 9744e2 | \([0, 1, 0, -17566568, 28332750372]\) | \(585442900448434507310500/40897317500487\) | \(41878853120498688\) | \([2]\) | \(430080\) | \(2.6432\) | |
| 9744.r2 | 9744e1 | \([0, 1, 0, -1095708, 444290220]\) | \(-568288203127281250000/4779437994366903\) | \(-1223536126557927168\) | \([2]\) | \(215040\) | \(2.2966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9744.r have rank \(1\).
Complex multiplication
The elliptic curves in class 9744.r do not have complex multiplication.Modular form 9744.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
