Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2541.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2541.a1 | 2541i1 | \([0, -1, 1, -1492, 20712]\) | \(25104437248/2470629\) | \(36172479189\) | \([]\) | \(4032\) | \(0.76280\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2541.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2541.a do not have complex multiplication.Modular form 2541.2.a.a
sage: E.q_eigenform(10)