Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.l3 23520bg1 [0, -1, 0, -3446, -75480] [2, 2] 36864 \(\Gamma_0(N)\)-optimal
23520.l4 23520bg2 [0, -1, 0, -16, -222284] [2] 73728  
23520.l2 23520bg3 [0, -1, 0, -7121, 117825] [2] 73728  
23520.l1 23520bg4 [0, -1, 0, -54896, -4932360] [2] 73728  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.bg

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} + 4q^{11} - 6q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 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.