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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4998u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.s1 | 4998u1 | \([1, 0, 1, -715279, 233372738]\) | \(-344002044213921241/1011143540736\) | \(-118960026424049664\) | \([]\) | \(97920\) | \(2.1468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4998u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4998u do not have complex multiplication.Modular form 4998.2.a.u
sage: E.q_eigenform(10)