Properties

Label 68544.y
Number of curves $4$
Conductor $68544$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 68544.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68544.y1 68544bf4 \([0, 0, 0, -2925516, -1925979536]\) \(14489843500598257/6246072\) \(1193642947510272\) \([2]\) \(1179648\) \(2.2356\)  
68544.y2 68544bf3 \([0, 0, 0, -391116, 49764976]\) \(34623662831857/14438442312\) \(2759229294627520512\) \([2]\) \(1179648\) \(2.2356\)  
68544.y3 68544bf2 \([0, 0, 0, -183756, -29778320]\) \(3590714269297/73410624\) \(14028988716417024\) \([2, 2]\) \(589824\) \(1.8890\)  
68544.y4 68544bf1 \([0, 0, 0, 564, -1393040]\) \(103823/4386816\) \(-838333592764416\) \([2]\) \(294912\) \(1.5424\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 68544.y have rank \(0\).

Complex multiplication

The elliptic curves in class 68544.y do not have complex multiplication.

Modular form 68544.2.a.y

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} + 6q^{13} - q^{17} + O(q^{20})\)  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.