Properties

Label 1003a
Number of curves $1$
Conductor $1003$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1003a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1003.b1 1003a1 \([0, -1, 1, 1, 1]\) \(32768/1003\) \(-1003\) \([]\) \(36\) \(-0.74408\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1003a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1003a do not have complex multiplication.

Modular form 1003.2.a.a

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