Properties

Label 168.b
Number of curves $4$
Conductor $168$
CM no
Rank $0$
Graph

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

Elliptic curves in class 168.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
168.b1 168a3 [0, 1, 0, -152, 672] [4] 32  
168.b2 168a2 [0, 1, 0, -12, 0] [2, 2] 16  
168.b3 168a1 [0, 1, 0, -7, -10] [2] 8 \(\Gamma_0(N)\)-optimal
168.b4 168a4 [0, 1, 0, 48, 48] [2] 32  

Rank

sage: E.rank()
 

The elliptic curves in class 168.b have rank \(0\).

Complex multiplication

The elliptic curves in class 168.b do not have complex multiplication.

Modular form 168.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} - q^{7} + q^{9} - 2q^{13} + 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.