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Properties

Label 158.b
Number of curves $3$
Conductor $158$
CM no
Rank $0$
Graph

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

Elliptic curves in class 158.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158.b1 158d2 \([1, 0, 1, -5217, -145452]\) \(15698803397448457/20709376\) \(20709376\) \([]\) \(120\) \(0.67986\)  
158.b2 158d1 \([1, 0, 1, -82, -92]\) \(59914169497/31554496\) \(31554496\) \([3]\) \(40\) \(0.13055\) \(\Gamma_0(N)\)-optimal
158.b3 158d3 \([1, 0, 1, -47, 118]\) \(11134383337/316\) \(316\) \([3]\) \(120\) \(-0.41875\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158.b have rank \(0\).

Complex multiplication

The elliptic curves in class 158.b do not have complex multiplication.

Modular form 158.2.a.b

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.