Properties

Label 1344.q
Number of curves $6$
Conductor $1344$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1344.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1344.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.q1 1344g4 [0, 1, 0, -86017, 9681503] [2] 3072  
1344.q2 1344g5 [0, 1, 0, -58497, -5412897] [2] 6144  
1344.q3 1344g3 [0, 1, 0, -6657, 71775] [2, 2] 3072  
1344.q4 1344g2 [0, 1, 0, -5377, 149855] [2, 2] 1536  
1344.q5 1344g1 [0, 1, 0, -257, 3423] [2] 768 \(\Gamma_0(N)\)-optimal
1344.q6 1344g6 [0, 1, 0, 24703, 579807] [4] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 1344.q have rank \(0\).

Modular form 1344.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} - q^{7} + q^{9} + 4q^{11} - 6q^{13} + 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.