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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 88200cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.bn1 | 88200cp1 | \([0, 0, 0, 48300, -12813500]\) | \(12459008/78125\) | \(-78139687500000000\) | \([]\) | \(645120\) | \(1.9233\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200cp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 88200cp do not have complex multiplication.Modular form 88200.2.a.cp
sage: E.q_eigenform(10)