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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 17160.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.q1 | 17160v2 | \([0, 1, 0, -9536, 264864]\) | \(46831495741058/11946352275\) | \(24466129459200\) | \([2]\) | \(55296\) | \(1.2786\) | |
| 17160.q2 | 17160v1 | \([0, 1, 0, 1464, 27264]\) | \(338649393884/498444375\) | \(-510407040000\) | \([2]\) | \(27648\) | \(0.93200\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17160.q have rank \(0\).
Complex multiplication
The elliptic curves in class 17160.q do not have complex multiplication.Modular form 17160.2.a.q
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.
