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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 405.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405.a1 | 405f1 | \([0, 0, 1, -3, -2]\) | \(36864/5\) | \(405\) | \([]\) | \(24\) | \(-0.77250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 405.a do not have complex multiplication.Modular form 405.2.a.a
sage: E.q_eigenform(10)