Properties

Label 1344.o
Number of curves $4$
Conductor $1344$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1344.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1344.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.o1 1344p4 [0, 1, 0, -7313, 238287] [2] 1152  
1344.o2 1344p3 [0, 1, 0, -453, 3675] [2] 576  
1344.o3 1344p2 [0, 1, 0, -113, 111] [2] 384  
1344.o4 1344p1 [0, 1, 0, 27, 27] [2] 192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1344.o have rank \(1\).

Modular form 1344.2.a.o

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.