↑

Properties

Label 22386.y
Number of curves $2$
Conductor $22386$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 22386.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22386.y1 22386w1 \([1, 0, 0, -155806, 23664452]\) \(-418288977642645996769/122877464621184\) \(-122877464621184\) \([7]\) \(131712\) \(1.6826\) \(\Gamma_0(N)\)-optimal
22386.y2 22386w2 \([1, 0, 0, 864584, -1045089598]\) \(71473535169369644529791/513262758348672548034\) \(-513262758348672548034\) \([]\) \(921984\) \(2.6555\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22386.y have rank \(0\).

Complex multiplication

The elliptic curves in class 22386.y do not have complex multiplication.

Modular form 22386.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.