Properties

Label 1002c
Number of curves $1$
Conductor $1002$
CM no
Rank $1$

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

Elliptic curves in class 1002c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1002.c1 1002c1 \([1, 0, 1, -3264, 71590]\) \(-3843995587427449/6390046584\) \(-6390046584\) \([]\) \(1008\) \(0.77740\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1002c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1002c do not have complex multiplication.

Modular form 1002.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} - 6 q^{13} + q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\)  Toggle raw display