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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 123840.gc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.gc1 | 123840dg1 | \([0, 0, 0, -12, 6896]\) | \(-2/215\) | \(-20543569920\) | \([]\) | \(86016\) | \(0.65771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840.gc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123840.gc do not have complex multiplication.Modular form 123840.2.a.gc
sage: E.q_eigenform(10)