Properties

Label 40425y
Number of curves 4
Conductor 40425
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("40425.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40425y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40425.p3 40425y1 [1, 1, 1, -7988, 269156] [2] 55296 \(\Gamma_0(N)\)-optimal
40425.p2 40425y2 [1, 1, 1, -14113, -208594] [2, 2] 110592  
40425.p4 40425y3 [1, 1, 1, 53262, -1556094] [2] 221184  
40425.p1 40425y4 [1, 1, 1, -179488, -29314594] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 40425y have rank \(1\).

Modular form 40425.2.a.p

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

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 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.