Properties

Label 187.b
Number of curves $1$
Conductor $187$
CM no
Rank $0$

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

Elliptic curves in class 187.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187.b1 187b1 \([0, 0, 1, 7, 1]\) \(37933056/22627\) \(-22627\) \([]\) \(30\) \(-0.47511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 187.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 187.b do not have complex multiplication.

Modular form 187.2.a.b

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