Properties

Label 186.b
Number of curves $1$
Conductor $186$
CM no
Rank $0$

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

Elliptic curves in class 186.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
186.b1 186c1 \([1, 0, 1, -17, -28]\) \(-498677257/11904\) \(-11904\) \([]\) \(28\) \(-0.43184\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 186.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 186.b do not have complex multiplication.

Modular form 186.2.a.b

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