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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 47190.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.u1 | 47190z1 | \([1, 0, 1, -729, -8714]\) | \(-24137569/4290\) | \(-7599996690\) | \([]\) | \(40320\) | \(0.62146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47190.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47190.u do not have complex multiplication.Modular form 47190.2.a.u
sage: E.q_eigenform(10)