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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 58800.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.ci1 | 58800bu2 | \([0, -1, 0, -1528, -22448]\) | \(4496182/9\) | \(790272000\) | \([2]\) | \(28672\) | \(0.59466\) | |
| 58800.ci2 | 58800bu1 | \([0, -1, 0, -128, -48]\) | \(5324/3\) | \(131712000\) | \([2]\) | \(14336\) | \(0.24808\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.ci do not have complex multiplication.Modular form 58800.2.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.
