Properties

Label 5010b
Number of curves $1$
Conductor $5010$
CM no
Rank $0$

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

Elliptic curves in class 5010b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5010.b1 5010b1 \([1, 1, 0, 3, -9]\) \(1685159/45090\) \(-45090\) \([]\) \(864\) \(-0.42684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5010b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5010b do not have complex multiplication.

Modular form 5010.2.a.b

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