Properties

Label 22386m
Number of curves 4
Conductor 22386
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("22386.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22386m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.n3 22386m1 [1, 0, 1, -235, -1402] [2] 7808 \(\Gamma_0(N)\)-optimal
22386.n2 22386m2 [1, 0, 1, -255, -1154] [2, 2] 15616  
22386.n4 22386m3 [1, 0, 1, 655, -7342] [2] 31232  
22386.n1 22386m4 [1, 0, 1, -1485, 20986] [2] 31232  

Rank

sage: E.rank()
 

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

Modular form 22386.2.a.n

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

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.