Properties

Label 44352.bj
Number of curves 6
Conductor 44352
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("44352.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44352.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44352.bj1 44352cf6 [0, 0, 0, -2602956, 1616397424] [2] 655360  
44352.bj2 44352cf4 [0, 0, 0, -163596, 24958960] [2, 2] 327680  
44352.bj3 44352cf2 [0, 0, 0, -22476, -724880] [2, 2] 163840  
44352.bj4 44352cf1 [0, 0, 0, -19596, -1055504] [2] 81920 \(\Gamma_0(N)\)-optimal
44352.bj5 44352cf5 [0, 0, 0, 17844, 77286256] [2] 655360  
44352.bj6 44352cf3 [0, 0, 0, 72564, -5248784] [2] 327680  

Rank

sage: E.rank()
 

The elliptic curves in class 44352.bj have rank \(1\).

Modular form 44352.2.a.bj

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.