Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1003.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1003.c1 1003b1 \([1, 0, 1, -8, -11]\) \(-47045881/17051\) \(-17051\) \([]\) \(48\) \(-0.47746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1003.2.a.c

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