Properties

Label 1003.c
Number of curves 1
Conductor 1003
CM no
Rank 0

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Show commands for: SageMath

sage: E = EllipticCurve("1003.c1")
sage: E.isogeny_class()

Elliptic curves in class 1003.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1003.c1 1003b1 [1, 0, 1, -8, -11] 1 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1003.c1 has rank \(0\).

Modular form 1003.2.a.c

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