Properties

Label 15680f
Number of curves $4$
Conductor $15680$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15680.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.bv4 15680f1 [0, 0, 0, 7252, 378672] [2] 36864 \(\Gamma_0(N)\)-optimal
15680.bv3 15680f2 [0, 0, 0, -55468, 4066608] [2, 2] 73728  
15680.bv2 15680f3 [0, 0, 0, -274988, -51867088] [2] 147456  
15680.bv1 15680f4 [0, 0, 0, -839468, 296028208] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 15680f have rank \(2\).

Modular form 15680.2.a.bv

sage: E.q_eigenform(10)
 
\( q - q^{5} - 3q^{9} - 4q^{11} - 6q^{13} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.