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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 40929.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40929.a1 | 40929a1 | \([0, -1, 1, -42, 110]\) | \(8390176768/859509\) | \(859509\) | \([]\) | \(17824\) | \(-0.12572\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40929.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 40929.a do not have complex multiplication.Modular form 40929.2.a.a
sage: E.q_eigenform(10)