Properties

Label 15680.k
Number of curves $2$
Conductor $15680$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.k1 15680x2 [0, 1, 0, -961, 7839] [2] 12288  
15680.k2 15680x1 [0, 1, 0, 159, 895] [2] 6144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 15680.k do not have complex multiplication.

Modular form 15680.2.a.k

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.