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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 5175.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5175.u1 | 5175p1 | \([1, -1, 0, -492, -1459]\) | \(46305/23\) | \(6549609375\) | \([]\) | \(1920\) | \(0.57653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5175.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5175.u do not have complex multiplication.Modular form 5175.2.a.u
sage: E.q_eigenform(10)