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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 236992.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.ci1 | 236992ci2 | \([0, -1, 0, -35904993, -12061596319]\) | \(263822189935250/149429406721\) | \(2899432579620642484256768\) | \([2]\) | \(32440320\) | \(3.3838\) | |
| 236992.ci2 | 236992ci1 | \([0, -1, 0, 8869567, -1503755071]\) | \(7953970437500/4703287687\) | \(-45629792188353658421248\) | \([2]\) | \(16220160\) | \(3.0373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.ci do not have complex multiplication.Modular form 236992.2.a.ci
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.
