Properties

Label 18240bn
Number of curves $4$
Conductor $18240$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18240.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18240bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18240.cp3 18240bn1 [0, 1, 0, -1985, 33183] [2] 12288 \(\Gamma_0(N)\)-optimal
18240.cp2 18240bn2 [0, 1, 0, -3265, -16225] [2, 2] 24576  
18240.cp1 18240bn3 [0, 1, 0, -39745, -3058657] [2] 49152  
18240.cp4 18240bn4 [0, 1, 0, 12735, -115425] [4] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 18240bn have rank \(0\).

Modular form 18240.2.a.cp

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.