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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 61710ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61710.co1 | 61710ck1 | \([1, 0, 0, -346486, 95402660]\) | \(-2596717791529849/718080000000\) | \(-1272122522880000000\) | \([]\) | \(1693440\) | \(2.1897\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61710ck1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61710ck do not have complex multiplication.Modular form 61710.2.a.ck
sage: E.q_eigenform(10)