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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 62400ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.gs2 | 62400ci1 | \([0, 1, 0, -43408, 11099438]\) | \(-9045718037056/48125390625\) | \(-48125390625000000\) | \([2]\) | \(442368\) | \(1.8852\) | \(\Gamma_0(N)\)-optimal |
| 62400.gs1 | 62400ci2 | \([0, 1, 0, -1059033, 418365063]\) | \(2052450196928704/4317958125\) | \(276349320000000000\) | \([2]\) | \(884736\) | \(2.2318\) |
Rank
sage: E.rank()
The elliptic curves in class 62400ci have rank \(0\).
Complex multiplication
The elliptic curves in class 62400ci do not have complex multiplication.Modular form 62400.2.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 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.
