Properties

Label 18097.b
Number of curves $1$
Conductor $18097$
CM no
Rank $1$

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

Elliptic curves in class 18097.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18097.b1 18097a1 \([1, 1, 1, -54, 130]\) \(17434421857/18097\) \(18097\) \([]\) \(1776\) \(-0.26537\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18097.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 18097.b do not have complex multiplication.

Modular form 18097.2.a.b

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