Properties

Label 1344r
Number of curves 6
Conductor 1344
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("1344.s1")
sage: E.isogeny_class()

Elliptic curves in class 1344r

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1344.s6 1344r1 [0, 1, 0, 63, 63] 2 256 \(\Gamma_0(N)\)-optimal
1344.s5 1344r2 [0, 1, 0, -257, 255] 4 512  
1344.s3 1344r3 [0, 1, 0, -2497, -48577] 2 1024  
1344.s2 1344r4 [0, 1, 0, -3137, 66495] 4 1024  
1344.s1 1344r5 [0, 1, 0, -50177, 4309503] 2 2048  
1344.s4 1344r6 [0, 1, 0, -2177, 108927] 2 2048  

Rank

sage: E.rank()

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

Modular form 1344.2.a.s

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.