Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 189618.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.k1 | 189618br1 | \([1, 1, 0, 727711, -49803723]\) | \(309147739823/186772608\) | \(-25748190057584472192\) | \([]\) | \(5031936\) | \(2.4138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 189618.k do not have complex multiplication.Modular form 189618.2.a.k
sage: E.q_eigenform(10)