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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 41405.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.s1 | 41405q1 | \([0, 0, 1, -637, 311015]\) | \(-1437696/2100875\) | \(-41771027445875\) | \([]\) | \(120960\) | \(1.2926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41405.s do not have complex multiplication.Modular form 41405.2.a.s
sage: E.q_eigenform(10)