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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 762a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
762.b1 | 762a1 | \([1, 0, 1, -6, -8]\) | \(-18609625/12192\) | \(-12192\) | \([]\) | \(60\) | \(-0.51495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 762a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 762a do not have complex multiplication.Modular form 762.2.a.a
sage: E.q_eigenform(10)