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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 52416gk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52416.ep1 | 52416gk1 | \([0, 0, 0, -4332, -126128]\) | \(-47045881/8736\) | \(-1669475598336\) | \([]\) | \(61440\) | \(1.0698\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 52416gk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 52416gk do not have complex multiplication.Modular form 52416.2.a.gk
sage: E.q_eigenform(10)