Show commands:
SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 19600ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.j1 | 19600ef1 | \([0, 0, 0, -140875, 22003450]\) | \(-1026590625/100352\) | \(-30224159866880000\) | \([]\) | \(304128\) | \(1.9032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600ef1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19600ef do not have complex multiplication.Modular form 19600.2.a.ef
sage: E.q_eigenform(10)