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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 27584.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.a1 | 27584bd1 | \([0, 0, 0, -4, 64]\) | \(-1728/431\) | \(-1765376\) | \([]\) | \(12032\) | \(-0.12211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27584.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 27584.a do not have complex multiplication.Modular form 27584.2.a.a
sage: E.q_eigenform(10)