Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.i3 23520bb1 [0, -1, 0, -1486, 21736] [2, 2] 18432 \(\Gamma_0(N)\)-optimal
23520.i4 23520bb2 [0, -1, 0, 719, 78625] [2] 36864  
23520.i2 23520bb3 [0, -1, 0, -3936, -65484] [2] 36864  
23520.i1 23520bb4 [0, -1, 0, -23536, 1397656] [2] 36864  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.bb

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

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.