Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.g1 23520bd4 [0, -1, 0, -7856, -265404] [2] 24576  
23520.g2 23520bd3 [0, -1, 0, -1976, 30360] [2] 24576  
23520.g3 23520bd1 [0, -1, 0, -506, -3744] [2, 2] 12288 \(\Gamma_0(N)\)-optimal
23520.g4 23520bd2 [0, -1, 0, 719, -20159] [2] 24576  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.