Properties

Label 4025.f
Number of curves 4
Conductor 4025
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4025.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4025.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4025.f1 4025c4 [1, -1, 0, -1052192, 415686091] [2] 34560  
4025.f2 4025c3 [1, -1, 0, -137942, -10015159] [2] 34560  
4025.f3 4025c2 [1, -1, 0, -66067, 6444216] [2, 2] 17280  
4025.f4 4025c1 [1, -1, 0, 58, 294591] [2] 8640 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4025.f have rank \(0\).

Modular form 4025.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + q^{7} - 3q^{8} - 3q^{9} - 4q^{11} + 2q^{13} + q^{14} - q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.