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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 88200.gk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.gk1 | 88200dd1 | \([0, 0, 0, 51450, -1860775]\) | \(358400/243\) | \(-10212172027470000\) | \([]\) | \(322560\) | \(1.7605\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200.gk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 88200.gk do not have complex multiplication.Modular form 88200.2.a.gk
sage: E.q_eigenform(10)