Properties

Label 29232ba
Number of curves $6$
Conductor $29232$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("29232.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29232ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29232.bk5 29232ba1 [0, 0, 0, -112899, 15632962] [2] 196608 \(\Gamma_0(N)\)-optimal
29232.bk4 29232ba2 [0, 0, 0, -1841619, 961934290] [2, 2] 393216  
29232.bk3 29232ba3 [0, 0, 0, -1876899, 923161570] [2, 2] 786432  
29232.bk1 29232ba4 [0, 0, 0, -29465859, 61563992002] [2] 786432  
29232.bk6 29232ba5 [0, 0, 0, 1797261, 4096900978] [2] 1572864  
29232.bk2 29232ba6 [0, 0, 0, -6115539, -4732031918] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 29232ba have rank \(1\).

Modular form 29232.2.a.bk

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.