Properties

Label 222768cl
Number of curves $2$
Conductor $222768$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 222768cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222768.fz1 222768cl1 \([0, 0, 0, -65523, 6452210]\) \(10418796526321/6390657\) \(19082399551488\) \([2]\) \(1146880\) \(1.4911\) \(\Gamma_0(N)\)-optimal
222768.fz2 222768cl2 \([0, 0, 0, -53283, 8936930]\) \(-5602762882081/8312741073\) \(-24821711840120832\) \([2]\) \(2293760\) \(1.8377\)  

Rank

sage: E.rank()
 

The elliptic curves in class 222768cl have rank \(0\).

Complex multiplication

The elliptic curves in class 222768cl do not have complex multiplication.

Modular form 222768.2.a.cl

sage: E.q_eigenform(10)
 
\(q + 4q^{5} - q^{7} - 4q^{11} + q^{13} - q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.