Properties

Label 23520.d
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 23520.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.d1 23520d4 \([0, -1, 0, -33336, -2330460]\) \(68017239368/39375\) \(2371803840000\) \([2]\) \(49152\) \(1.3201\)  
23520.d2 23520d3 \([0, -1, 0, -19616, 1048776]\) \(13858588808/229635\) \(13832359994880\) \([2]\) \(49152\) \(1.3201\)  
23520.d3 23520d1 \([0, -1, 0, -2466, -21384]\) \(220348864/99225\) \(747118209600\) \([2, 2]\) \(24576\) \(0.97357\) \(\Gamma_0(N)\)-optimal
23520.d4 23520d2 \([0, -1, 0, 8559, -169119]\) \(143877824/108045\) \(-52065837895680\) \([2]\) \(49152\) \(1.3201\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.