Properties

Label 11197a
Number of curves 1
Conductor 11197
CM no
Rank 3

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("11197.a1")
sage: E.isogeny_class()

Elliptic curves in class 11197a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
11197.a1 11197a1 [1, -1, 1, -6, 0] 1 2080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 11197a1 has rank \(3\).

Modular form 11197.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} - 3q^{3} - q^{4} - 2q^{5} + 3q^{6} - 5q^{7} + 3q^{8} + 6q^{9} + 2q^{10} - 4q^{11} + 3q^{12} - 7q^{13} + 5q^{14} + 6q^{15} - q^{16} - 2q^{17} - 6q^{18} - 5q^{19} + O(q^{20}) \)