Properties

Label 8925d
Number of curves 4
Conductor 8925
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8925.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8925d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8925.v4 8925d1 [1, 1, 0, 350, 4375] [2] 6144 \(\Gamma_0(N)\)-optimal
8925.v3 8925d2 [1, 1, 0, -2775, 45000] [2, 2] 12288  
8925.v2 8925d3 [1, 1, 0, -13400, -560625] [2] 24576  
8925.v1 8925d4 [1, 1, 0, -42150, 3313125] [4] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 8925d have rank \(0\).

Modular form 8925.2.a.v

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.