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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 51376.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51376.f1 | 51376y1 | \([0, 1, 0, -784, 8724]\) | \(-77086633/5776\) | \(-3998285824\) | \([]\) | \(41472\) | \(0.59098\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51376.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 51376.f do not have complex multiplication.Modular form 51376.2.a.f
sage: E.q_eigenform(10)