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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 5610.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.s1 | 5610u1 | \([1, 0, 1, 777, -123494]\) | \(51974460932759/6625297800000\) | \(-6625297800000\) | \([]\) | \(15840\) | \(1.1395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5610.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5610.s do not have complex multiplication.Modular form 5610.2.a.s
sage: E.q_eigenform(10)