↑

Properties

Label 116610.k
Number of curves $2$
Conductor $116610$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 116610.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116610.k1 116610v2 \([1, 1, 0, -525365402, -4635053223276]\) \(3322370073744239033417329/54039020920560000\) \(260836032530547293040000\) \([2]\) \(32514048\) \(3.6254\)  
116610.k2 116610v1 \([1, 1, 0, -31831322, -77068580844]\) \(-738971428463935080049/103763447735500800\) \(-500846343400744880947200\) \([2]\) \(16257024\) \(3.2788\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116610.k have rank \(1\).

Complex multiplication

The elliptic curves in class 116610.k do not have complex multiplication.

Modular form 116610.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} + 2 q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.