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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 27200.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27200.ci1 | 27200cl4 | \([0, -1, 0, -180833, 20513537]\) | \(159661140625/48275138\) | \(197734965248000000\) | \([2]\) | \(331776\) | \(2.0239\) | |
| 27200.ci2 | 27200cl3 | \([0, -1, 0, -164833, 25809537]\) | \(120920208625/19652\) | \(80494592000000\) | \([2]\) | \(165888\) | \(1.6774\) | |
| 27200.ci3 | 27200cl2 | \([0, -1, 0, -68833, -6926463]\) | \(8805624625/2312\) | \(9469952000000\) | \([2]\) | \(110592\) | \(1.4746\) | |
| 27200.ci4 | 27200cl1 | \([0, -1, 0, -4833, -78463]\) | \(3048625/1088\) | \(4456448000000\) | \([2]\) | \(55296\) | \(1.1280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27200.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 27200.ci do not have complex multiplication.Modular form 27200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
