Properties

Label 44352ea
Number of curves 6
Conductor 44352
CM no
Rank 2
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("44352.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44352ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44352.bc4 44352ea1 [0, 0, 0, -19596, 1055504] [2] 81920 \(\Gamma_0(N)\)-optimal
44352.bc3 44352ea2 [0, 0, 0, -22476, 724880] [2, 2] 163840  
44352.bc6 44352ea3 [0, 0, 0, 72564, 5248784] [2] 327680  
44352.bc2 44352ea4 [0, 0, 0, -163596, -24958960] [2, 2] 327680  
44352.bc5 44352ea5 [0, 0, 0, 17844, -77286256] [2] 655360  
44352.bc1 44352ea6 [0, 0, 0, -2602956, -1616397424] [2] 655360  

Rank

sage: E.rank()
 

The elliptic curves in class 44352ea have rank \(2\).

Modular form 44352.2.a.bc

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

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 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.