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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 786a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
786.c1 | 786a1 | \([1, 1, 0, -8, 6]\) | \(68417929/786\) | \(786\) | \([]\) | \(40\) | \(-0.63150\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 786a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 786a do not have complex multiplication.Modular form 786.2.a.a
sage: E.q_eigenform(10)