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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 762c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
762.a1 | 762c1 | \([1, 0, 1, -10, -10]\) | \(95443993/20574\) | \(20574\) | \([]\) | \(96\) | \(-0.45829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 762c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 762c do not have complex multiplication.Modular form 762.2.a.c
sage: E.q_eigenform(10)