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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 47190j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.k1 | 47190j1 | \([1, 1, 0, -442862, 163578804]\) | \(-4073768343611/2555904000\) | \(-6026687935217664000\) | \([]\) | \(1083456\) | \(2.3052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47190j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47190j do not have complex multiplication.Modular form 47190.2.a.j
sage: E.q_eigenform(10)