Properties

Label 1003.d
Number of curves 1
Conductor 1003
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("1003.d1")
sage: E.isogeny_class()

Elliptic curves in class 1003.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1003.d1 1003d1 [0, 0, 1, -41, 135] 1 180 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1003.d1 has rank \(1\).

Modular form 1003.2.a.d

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