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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 466752.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 466752.ci1 | 466752ci1 | \([0, 1, 0, -5985, 124959]\) | \(90458382169/25788048\) | \(6760182054912\) | \([2]\) | \(1228800\) | \(1.1685\) | \(\Gamma_0(N)\)-optimal |
| 466752.ci2 | 466752ci2 | \([0, 1, 0, 15775, 843039]\) | \(1656015369191/2114999172\) | \(-554434342944768\) | \([2]\) | \(2457600\) | \(1.5150\) |
Rank
sage: E.rank()
The elliptic curves in class 466752.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 466752.ci do not have complex multiplication.Modular form 466752.2.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.
