Properties

Label 106b
Number of curves $1$
Conductor $106$
CM no
Rank $1$

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

Elliptic curves in class 106b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106.a1 106b1 \([1, 1, 0, -7, 5]\) \(-47045881/848\) \(-848\) \([]\) \(8\) \(-0.64173\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 106b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 106b do not have complex multiplication.

Modular form 106.2.a.b

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