Properties

Label 4002.r
Number of curves 1
Conductor 4002
CM no
Rank 0

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("4002.r1")
sage: E.isogeny_class()

Elliptic curves in class 4002.r

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4002.r1 4002p1 [1, 0, 0, -1811224, 938072696] 1 33120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 4002.r1 has rank \(0\).

Modular form 4002.2.a.r

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