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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 73689.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73689.u1 | 73689n1 | \([1, 1, 0, -40797451, 100287457516]\) | \(-289531596860402017/17410522563\) | \(-451584116241821772363\) | \([]\) | \(5322240\) | \(3.0244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 73689.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 73689.u do not have complex multiplication.Modular form 73689.2.a.u
sage: E.q_eigenform(10)