Properties

Label 10002.b
Number of curves $1$
Conductor $10002$
CM no
Rank $0$

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

Elliptic curves in class 10002.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10002.b1 10002b1 \([1, 1, 0, -810, 8532]\) \(58886570067625/92178432\) \(92178432\) \([]\) \(5280\) \(0.42682\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10002.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 10002.b do not have complex multiplication.

Modular form 10002.2.a.b

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