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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 5610.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.k1 | 5610l1 | \([1, 0, 1, -2864, -71938]\) | \(-2596717791529849/718080000000\) | \(-718080000000\) | \([]\) | \(14112\) | \(0.99076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5610.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5610.k do not have complex multiplication.Modular form 5610.2.a.k
sage: E.q_eigenform(10)