Properties

Label 106.b
Number of curves $1$
Conductor $106$
CM no
Rank $0$

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

Elliptic curves in class 106.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106.b1 106d1 \([1, 1, 0, -27, -67]\) \(-2305199161/1696\) \(-1696\) \([]\) \(10\) \(-0.44626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 106.b1 has rank \(0\).

Complex multiplication

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

Modular form 106.2.a.b

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