Properties

Label 10002.c
Number of curves 1
Conductor 10002
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("10002.c1")
sage: E.isogeny_class()

Elliptic curves in class 10002.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10002.c1 10002a1 [1, 1, 0, -1804, 32080] 1 14560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10002.c1 has rank \(1\).

Modular form 10002.2.a.c

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