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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 174570ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
174570.r1 | 174570ck1 | \([1, 1, 0, -6119747, -18404628141]\) | \(-14072579252207/73076891250\) | \(-131622637166379716898750\) | \([]\) | \(19783680\) | \(3.1204\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 174570ck1 has rank \(1\).
Complex multiplication
The elliptic curves in class 174570ck do not have complex multiplication.Modular form 174570.2.a.ck
sage: E.q_eigenform(10)