Properties

Label 13680.bk
Number of curves $4$
Conductor $13680$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("13680.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13680.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13680.bk1 13680br3 [0, 0, 0, -89427, -10278254] [2] 49152  
13680.bk2 13680br2 [0, 0, 0, -7347, -51086] [2, 2] 24576  
13680.bk3 13680br1 [0, 0, 0, -4467, 114226] [2] 12288 \(\Gamma_0(N)\)-optimal
13680.bk4 13680br4 [0, 0, 0, 28653, -403886] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 13680.bk have rank \(1\).

Modular form 13680.2.a.bk

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.