Properties

Label 18240.bo
Number of curves $4$
Conductor $18240$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18240.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18240.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18240.bo1 18240cm3 [0, 1, 0, -194561, -33096705] [2] 73728  
18240.bo2 18240cm4 [0, 1, 0, -14081, -346881] [2] 73728  
18240.bo3 18240cm2 [0, 1, 0, -12161, -520065] [2, 2] 36864  
18240.bo4 18240cm1 [0, 1, 0, -641, -10881] [2] 18432 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18240.bo have rank \(1\).

Modular form 18240.2.a.bo

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} - 4q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} - q^{19} + O(q^{20}) \)

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.