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SageMath
E = EllipticCurve("ls1")
E.isogeny_class()
Elliptic curves in class 366912.ls
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366912.ls1 | 366912ls2 | \([0, 0, 0, -25284, 1240288]\) | \(5088448/1053\) | \(369916827291648\) | \([2]\) | \(1474560\) | \(1.5105\) | |
366912.ls2 | 366912ls1 | \([0, 0, 0, 3381, 116620]\) | \(778688/1521\) | \(-8348817282624\) | \([2]\) | \(737280\) | \(1.1640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 366912.ls have rank \(1\).
Complex multiplication
The elliptic curves in class 366912.ls do not have complex multiplication.Modular form 366912.2.a.ls
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.