Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 284592.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.x1 | 284592x1 | \([0, -1, 0, -173917, -21517439]\) | \(90112/21\) | \(135577924558374144\) | \([]\) | \(2433024\) | \(1.9993\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 284592.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 284592.x do not have complex multiplication.Modular form 284592.2.a.x
sage: E.q_eigenform(10)