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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 215600.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.cp1 | 215600ca1 | \([0, -1, 0, -4920008, -3808041488]\) | \(85713473128801/8800000000\) | \(1352243200000000000000\) | \([]\) | \(7299072\) | \(2.7902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 215600.cp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 215600.cp do not have complex multiplication.Modular form 215600.2.a.cp
sage: E.q_eigenform(10)