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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 41405j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.c1 | 41405j1 | \([0, 0, 1, -107653, 683300504]\) | \(-1437696/2100875\) | \(-201620771214996462875\) | \([]\) | \(1572480\) | \(2.5751\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41405j do not have complex multiplication.Modular form 41405.2.a.j
sage: E.q_eigenform(10)