Properties

Label 190.b
Number of curves $1$
Conductor $190$
CM no
Rank $1$

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

Elliptic curves in class 190.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190.b1 190a1 \([1, -1, 1, -48, 147]\) \(-11993263569/972800\) \(-972800\) \([]\) \(88\) \(-0.10478\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 190.b do not have complex multiplication.

Modular form 190.2.a.b

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