Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 86394.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86394.r1 | 86394e1 | \([1, 1, 0, -1695333, 1004093325]\) | \(-2513898149714809/579901980672\) | \(-124307139666533548032\) | \([]\) | \(7037184\) | \(2.5754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 86394.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 86394.r do not have complex multiplication.Modular form 86394.2.a.r
sage: E.q_eigenform(10)