Properties

Label 23520d
Number of curves $4$
Conductor $23520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.d3 23520d1 [0, -1, 0, -2466, -21384] [2, 2] 24576 \(\Gamma_0(N)\)-optimal
23520.d4 23520d2 [0, -1, 0, 8559, -169119] [2] 49152  
23520.d2 23520d3 [0, -1, 0, -19616, 1048776] [2] 49152  
23520.d1 23520d4 [0, -1, 0, -33336, -2330460] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 23520d have rank \(0\).

Complex multiplication

The elliptic curves in class 23520d do not have complex multiplication.

Modular form 23520.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.