Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 169050.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.j1 | 169050id1 | \([1, 1, 0, -3455, -78315]\) | \(1551443665/29808\) | \(87672034800\) | \([]\) | \(253440\) | \(0.89275\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169050.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169050.j do not have complex multiplication.Modular form 169050.2.a.j
sage: E.q_eigenform(10)