Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2001.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2001.a1 | 2001a1 | \([1, 1, 1, 11, -52]\) | \(146363183/1458729\) | \(-1458729\) | \([]\) | \(280\) | \(-0.13612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2001.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 2001.a do not have complex multiplication.Modular form 2001.2.a.a
sage: E.q_eigenform(10)