Properties

Label 206910be
Number of curves $4$
Conductor $206910$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("206910.cy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 206910be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206910.cy4 206910be1 [1, -1, 1, -10913, 751457] [2] 983040 \(\Gamma_0(N)\)-optimal
206910.cy3 206910be2 [1, -1, 1, -206933, 36270281] [2, 2] 1966080  
206910.cy1 206910be3 [1, -1, 1, -3310583, 2319315221] [2] 3932160  
206910.cy2 206910be4 [1, -1, 1, -239603, 24077837] [2] 3932160  

Rank

sage: E.rank()
 

The elliptic curves in class 206910be have rank \(1\).

Modular form 206910.2.a.cy

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} - 4q^{7} + q^{8} - q^{10} + 2q^{13} - 4q^{14} + q^{16} - 2q^{17} + q^{19} + O(q^{20}) \)

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.