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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 41405s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.t1 | 41405s1 | \([0, 0, 1, -57967, -9231245]\) | \(-110592/125\) | \(-24347394181257875\) | \([]\) | \(753984\) | \(1.8387\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41405s do not have complex multiplication.Modular form 41405.2.a.s
sage: E.q_eigenform(10)