Properties

Label 46800.de
Number of curves $6$
Conductor $46800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("46800.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46800.de1 46800cx6 [0, 0, 0, -32454075, -71162617750] [2] 2359296  
46800.de2 46800cx4 [0, 0, 0, -3042075, 2040610250] [2] 1179648  
46800.de3 46800cx3 [0, 0, 0, -2034075, -1105357750] [2, 2] 1179648  
46800.de4 46800cx5 [0, 0, 0, -414075, -2817697750] [2] 2359296  
46800.de5 46800cx2 [0, 0, 0, -234075, 16042250] [2, 2] 589824  
46800.de6 46800cx1 [0, 0, 0, 53925, 1930250] [2] 294912 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.de have rank \(1\).

Modular form 46800.2.a.de

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.