Properties

Label 116928dw
Number of curves $6$
Conductor $116928$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("116928.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116928dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116928.r5 116928dw1 [0, 0, 0, -451596, 125063696] [2] 1572864 \(\Gamma_0(N)\)-optimal
116928.r4 116928dw2 [0, 0, 0, -7366476, 7695474320] [2, 2] 3145728  
116928.r3 116928dw3 [0, 0, 0, -7507596, 7385292560] [2, 2] 6291456  
116928.r1 116928dw4 [0, 0, 0, -117863436, 492511936016] [2] 6291456  
116928.r6 116928dw5 [0, 0, 0, 7189044, 32775207824] [2] 12582912  
116928.r2 116928dw6 [0, 0, 0, -24462156, -37856255344] [2] 12582912  

Rank

sage: E.rank()
 

The elliptic curves in class 116928dw have rank \(0\).

Modular form 116928.2.a.r

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.