Properties

Label 100014.b
Number of curves $1$
Conductor $100014$
CM no
Rank $2$

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

Elliptic curves in class 100014.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100014.b1 100014b1 \([1, 1, 1, -107, 377]\) \(135559106353/1600224\) \(1600224\) \([]\) \(25760\) \(0.0023165\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100014.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 100014.b do not have complex multiplication.

Modular form 100014.2.a.b

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