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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 15680.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.u1 | 15680de1 | \([0, 1, 0, -47105, -4592897]\) | \(-15298178/3125\) | \(-2361262489600000\) | \([]\) | \(80640\) | \(1.6721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 15680.u do not have complex multiplication.Modular form 15680.2.a.u
sage: E.q_eigenform(10)