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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 16560.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.j1 | 16560bh2 | \([0, 0, 0, -565203, -163551598]\) | \(6687281588245201/165600\) | \(494478950400\) | \([2]\) | \(92160\) | \(1.7624\) | |
16560.j2 | 16560bh1 | \([0, 0, 0, -35283, -2561902]\) | \(-1626794704081/8125440\) | \(-24262433832960\) | \([2]\) | \(46080\) | \(1.4158\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.j have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.j do not have complex multiplication.Modular form 16560.2.a.j
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.