Properties

Label 84966.ct
Number of curves $4$
Conductor $84966$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84966.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.ct1 84966cw4 \([1, 1, 1, -71924014, -234808740685]\) \(14489843500598257/6246072\) \(17737350764866706232\) \([2]\) \(10616832\) \(3.0361\)  
84966.ct2 84966cw3 \([1, 1, 1, -9615614, 6062392307]\) \(34623662831857/14438442312\) \(41001723288850499049672\) \([2]\) \(10616832\) \(3.0361\)  
84966.ct3 84966cw2 \([1, 1, 1, -4517654, -3631888429]\) \(3590714269297/73410624\) \(208468616396951905344\) \([2, 2]\) \(5308416\) \(2.6895\)  
84966.ct4 84966cw1 \([1, 1, 1, 13866, -169807149]\) \(103823/4386816\) \(-12457508356120375296\) \([4]\) \(2654208\) \(2.3430\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 84966.ct have rank \(1\).

Complex multiplication

The elliptic curves in class 84966.ct do not have complex multiplication.

Modular form 84966.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} + q^{8} + q^{9} - 2q^{10} - q^{12} + 6q^{13} + 2q^{15} + q^{16} + q^{18} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.