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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2646.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2646.a1 | 2646g3 | \([1, -1, 0, -6036, 240848]\) | \(-1167051/512\) | \(-10670677710336\) | \([]\) | \(6804\) | \(1.2071\) | |
| 2646.a2 | 2646g1 | \([1, -1, 0, -156, -722]\) | \(-132651/2\) | \(-6353046\) | \([]\) | \(756\) | \(0.10844\) | \(\Gamma_0(N)\)-optimal |
| 2646.a3 | 2646g2 | \([1, -1, 0, 579, -3907]\) | \(9261/8\) | \(-18525482136\) | \([]\) | \(2268\) | \(0.65775\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.a do not have complex multiplication.Modular form 2646.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
