Properties

Label 23184bi
Number of curves $6$
Conductor $23184$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23184.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23184bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23184.bk5 23184bi1 [0, 0, 0, 18141, 1926178] [2] 98304 \(\Gamma_0(N)\)-optimal
23184.bk4 23184bi2 [0, 0, 0, -166179, 22311970] [2, 2] 196608  
23184.bk3 23184bi3 [0, 0, 0, -730659, -218720990] [2, 2] 393216  
23184.bk2 23184bi4 [0, 0, 0, -2550819, 1568035618] [2] 393216  
23184.bk6 23184bi5 [0, 0, 0, 902301, -1057735838] [2] 786432  
23184.bk1 23184bi6 [0, 0, 0, -11395299, -14805815582] [2] 786432  

Rank

sage: E.rank()
 

The elliptic curves in class 23184bi have rank \(1\).

Modular form 23184.2.a.bk

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.