Properties

Label 23520.h
Number of curves $4$
Conductor $23520$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.h1 23520bc4 [0, -1, 0, -691896, 221748696] [2] 147456  
23520.h2 23520bc3 [0, -1, 0, -109776, -9315900] [2] 147456  
23520.h3 23520bc1 [0, -1, 0, -43626, 3411360] [2, 2] 73728 \(\Gamma_0(N)\)-optimal
23520.h4 23520bc2 [0, -1, 0, 16399, 12018945] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.h have rank \(1\).

Complex multiplication

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

Modular form 23520.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.