Properties

Label 1002.b
Number of curves $1$
Conductor $1002$
CM no
Rank $0$

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

Elliptic curves in class 1002.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1002.b1 1002b1 \([1, 1, 0, 564, 1872]\) \(19785968032823/12608077824\) \(-12608077824\) \([]\) \(1104\) \(0.62711\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1002.b1 has rank \(0\).

Complex multiplication

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

Modular form 1002.2.a.b

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