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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 127680.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127680.u1 | 127680eg1 | \([0, -1, 0, 75999, 6200001]\) | \(185183253170999/171032148000\) | \(-44835051405312000\) | \([]\) | \(1105920\) | \(1.8824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 127680.u1 has rank \(2\).
Complex multiplication
The elliptic curves in class 127680.u do not have complex multiplication.Modular form 127680.2.a.u
sage: E.q_eigenform(10)