Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1003.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1003.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1003.b1 1003a1 [0, -1, 1, 1, 1] [] 36 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1003.b1 has rank \(1\).

Modular form 1003.2.a.b

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