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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 51600ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.c1 | 51600ck1 | \([0, -1, 0, -192833, -35072088]\) | \(-126879079874560/11907683883\) | \(-74423024268750000\) | \([]\) | \(489600\) | \(1.9794\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51600ck1 has rank \(1\).
Complex multiplication
The elliptic curves in class 51600ck do not have complex multiplication.Modular form 51600.2.a.ck
sage: E.q_eigenform(10)