Properties

Label 25410.bu
Number of curves $4$
Conductor $25410$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25410.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25410.bu1 25410bt4 [1, 1, 1, -45196, -3717097] [2] 81920  
25410.bu2 25410bt2 [1, 1, 1, -2846, -58057] [2, 2] 40960  
25410.bu3 25410bt1 [1, 1, 1, -426, 1959] [2] 20480 \(\Gamma_0(N)\)-optimal
25410.bu4 25410bt3 [1, 1, 1, 784, -191641] [2] 81920  

Rank

sage: E.rank()
 

The elliptic curves in class 25410.bu have rank \(0\).

Complex multiplication

The elliptic curves in class 25410.bu do not have complex multiplication.

Modular form 25410.2.a.bu

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

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 LMFDB 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 LMFDB labels.