Properties

Label 17640bd
Number of curves $6$
Conductor $17640$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17640.cq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17640bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17640.cq4 17640bd1 [0, 0, 0, -77322, 8275561] [4] 49152 \(\Gamma_0(N)\)-optimal
17640.cq3 17640bd2 [0, 0, 0, -79527, 7778554] [2, 2] 98304  
17640.cq2 17640bd3 [0, 0, 0, -300027, -54887546] [2, 2] 196608  
17640.cq5 17640bd4 [0, 0, 0, 105693, 38636206] [2] 196608  
17640.cq1 17640bd5 [0, 0, 0, -4621827, -3824361506] [2] 393216  
17640.cq6 17640bd6 [0, 0, 0, 493773, -296043986] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 17640bd have rank \(0\).

Modular form 17640.2.a.cq

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

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.