Properties

Label 25410n
Number of curves $6$
Conductor $25410$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("25410.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25410n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25410.n6 25410n1 [1, 1, 0, 1208, 23104] [2] 40960 \(\Gamma_0(N)\)-optimal
25410.n5 25410n2 [1, 1, 0, -8472, 230256] [2, 2] 81920  
25410.n4 25410n3 [1, 1, 0, -44772, -3465084] [2] 163840  
25410.n2 25410n4 [1, 1, 0, -127052, 17376924] [2, 2] 163840  
25410.n3 25410n5 [1, 1, 0, -118582, 19804426] [2] 327680  
25410.n1 25410n6 [1, 1, 0, -2032802, 1114707774] [2] 327680  

Rank

sage: E.rank()
 

The elliptic curves in class 25410n have rank \(1\).

Modular form 25410.2.a.n

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.