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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 41405.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41405.a1 | 41405t1 | \([0, 0, 1, -637, -32328]\) | \(-1437696/21875\) | \(-434933646875\) | \([]\) | \(144000\) | \(0.91459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41405.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41405.a do not have complex multiplication.Modular form 41405.2.a.a
sage: E.q_eigenform(10)