Properties

Label 169650eo
Number of curves $4$
Conductor $169650$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 169650eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169650.cx3 169650eo1 \([1, -1, 0, -398817, -96838659]\) \(615882348586441/21715200\) \(247349700000000\) \([2]\) \(2359296\) \(1.8516\) \(\Gamma_0(N)\)-optimal
169650.cx2 169650eo2 \([1, -1, 0, -416817, -87604659]\) \(703093388853961/115124490000\) \(1311339893906250000\) \([2, 2]\) \(4718592\) \(2.1982\)  
169650.cx1 169650eo3 \([1, -1, 0, -1879317, 908357841]\) \(64443098670429961/6032611833300\) \(68715219163682812500\) \([2]\) \(9437184\) \(2.5448\)  
169650.cx4 169650eo4 \([1, -1, 0, 757683, -492807159]\) \(4223169036960119/11647532812500\) \(-132672678442382812500\) \([2]\) \(9437184\) \(2.5448\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169650eo have rank \(0\).

Complex multiplication

The elliptic curves in class 169650eo do not have complex multiplication.

Modular form 169650.2.a.eo

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} + 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\)  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 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.