Properties

Label 1344.g
Number of curves 6
Conductor 1344
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1344.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1344.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.g1 1344a5 [0, -1, 0, -50177, -4309503] [2] 2048  
1344.g2 1344a3 [0, -1, 0, -3137, -66495] [2, 2] 1024  
1344.g3 1344a4 [0, -1, 0, -2497, 48577] [2] 1024  
1344.g4 1344a6 [0, -1, 0, -2177, -108927] [2] 2048  
1344.g5 1344a2 [0, -1, 0, -257, -255] [2, 2] 512  
1344.g6 1344a1 [0, -1, 0, 63, -63] [2] 256 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 1344.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.