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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 47190.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.j1 | 47190p1 | \([1, 1, 0, -2, 114]\) | \(-121/390\) | \(-5709990\) | \([]\) | \(13440\) | \(-0.024579\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47190.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47190.j do not have complex multiplication.Modular form 47190.2.a.j
sage: E.q_eigenform(10)