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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 43200gk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43200.in1 | 43200gk1 | \([0, 0, 0, -1350, -20250]\) | \(-13824\) | \(-19683000000\) | \([]\) | \(36864\) | \(0.72485\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 43200gk1 has rank \(0\).
Complex multiplication
The elliptic curves in class 43200gk do not have complex multiplication.Modular form 43200.2.a.gk
sage: E.q_eigenform(10)