Properties

Label 144.b
Number of curves $6$
Conductor $144$
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 144.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
144.b1 144b5 [0, 0, 0, -3459, -78302] [2] 64  
144.b2 144b4 [0, 0, 0, -579, 5362] [4] 32  
144.b3 144b3 [0, 0, 0, -219, -1190] [2, 2] 32  
144.b4 144b2 [0, 0, 0, -39, 70] [2, 2] 16  
144.b5 144b1 [0, 0, 0, 6, 7] [2] 8 \(\Gamma_0(N)\)-optimal
144.b6 144b6 [0, 0, 0, 141, -4718] [2] 64  

Rank

sage: E.rank()
 

The elliptic curves in class 144.b have rank \(0\).

Complex multiplication

The elliptic curves in class 144.b do not have complex multiplication.

Modular form 144.2.a.b

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.