Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 8050j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8050.i1 | 8050j1 | \([1, -1, 0, 268, 33946]\) | \(84972077055/20040095362\) | \(-501002384050\) | \([]\) | \(8064\) | \(0.92419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8050j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8050j do not have complex multiplication.Modular form 8050.2.a.j
sage: E.q_eigenform(10)