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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 55545.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55545.s1 | 55545y1 | \([0, 1, 1, 15430225, 52499028281]\) | \(2744564518708084736/9629735831296875\) | \(-1425546504621186913546875\) | \([]\) | \(4942080\) | \(3.3177\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55545.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55545.s do not have complex multiplication.Modular form 55545.2.a.s
sage: E.q_eigenform(10)