Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 20097.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20097.j1 | 20097c1 | \([1, -1, 0, -2364, -77833]\) | \(-74246873427/92019697\) | \(-1811223696051\) | \([]\) | \(22464\) | \(1.0456\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20097.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 20097.j do not have complex multiplication.Modular form 20097.2.a.j
sage: E.q_eigenform(10)