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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 47190.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.x1 | 47190w1 | \([1, 0, 1, -69369, -7038308]\) | \(-305088363822419089/15974400000\) | \(-1932902400000\) | \([]\) | \(163200\) | \(1.4260\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47190.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47190.x do not have complex multiplication.Modular form 47190.2.a.x
sage: E.q_eigenform(10)