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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 41405a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.n1 | 41405a1 | \([1, 1, 0, -8453, -4588618]\) | \(-2401/325\) | \(-9043317838752925\) | \([]\) | \(282240\) | \(1.7412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41405a do not have complex multiplication.Modular form 41405.2.a.a
sage: E.q_eigenform(10)