Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 17661e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17661.i1 | 17661e1 | \([1, 0, 1, -18, 19]\) | \(707281/189\) | \(158949\) | \([]\) | \(1440\) | \(-0.29365\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 17661e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 17661e do not have complex multiplication.Modular form 17661.2.a.e
sage: E.q_eigenform(10)