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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 457136.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457136.a1 | 457136a1 | \([0, 1, 0, -69, -589]\) | \(-8998912/28571\) | \(-117026816\) | \([]\) | \(169600\) | \(0.23465\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 457136.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 457136.a do not have complex multiplication.Modular form 457136.2.a.a
sage: E.q_eigenform(10)