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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1264.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1264.a1 | 1264i2 | \([0, 1, 0, -144, -620]\) | \(81182737/12482\) | \(51126272\) | \([2]\) | \(288\) | \(0.20268\) | |
| 1264.a2 | 1264i1 | \([0, 1, 0, 16, -44]\) | \(103823/316\) | \(-1294336\) | \([2]\) | \(144\) | \(-0.14389\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1264.a have rank \(1\).
Complex multiplication
The elliptic curves in class 1264.a do not have complex multiplication.Modular form 1264.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
