Properties

Label 53a
Number of curves 1
Conductor 53
CM no
Rank 1

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("53.a1")
sage: E.isogeny_class()

Elliptic curves in class 53a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
53.a1 53a1 [1, -1, 1, 0, 0] 1 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 53a1 has rank \(1\).

Modular form 53.2.a.a

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