Properties

Label 25270c
Number of curves $4$
Conductor $25270$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25270.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25270c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25270.e4 25270c1 [1, -1, 0, 835, 14581] [2] 28800 \(\Gamma_0(N)\)-optimal
25270.e3 25270c2 [1, -1, 0, -6385, 160425] [2, 2] 57600  
25270.e2 25270c3 [1, -1, 0, -31655, -2017849] [2] 115200  
25270.e1 25270c4 [1, -1, 0, -96635, 11586075] [2] 115200  

Rank

sage: E.rank()
 

The elliptic curves in class 25270c have rank \(0\).

Modular form 25270.2.a.e

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

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 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.