Properties

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

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

Elliptic curves in class 15680.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.k1 15680x2 \([0, 1, 0, -961, 7839]\) \(2185454/625\) \(28098560000\) \([2]\) \(12288\) \(0.71147\)  
15680.k2 15680x1 \([0, 1, 0, 159, 895]\) \(19652/25\) \(-561971200\) \([2]\) \(6144\) \(0.36490\) \(\Gamma_0(N)\)-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)
 
\(q - 2 q^{3} - q^{5} + q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.