Properties

Label 284592.eu
Number of curves 6
Conductor 284592
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("284592.eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 284592.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
284592.eu1 284592eu5 [0, -1, 0, -428692392, 3416526069552] [2] 58982400  
284592.eu2 284592eu3 [0, -1, 0, -26943352, 52761707440] [2, 2] 29491200  
284592.eu3 284592eu2 [0, -1, 0, -3701672, -1530857040] [2, 2] 14745600  
284592.eu4 284592eu1 [0, -1, 0, -3227352, -2229814992] [2] 7372800 \(\Gamma_0(N)\)-optimal
284592.eu5 284592eu6 [0, -1, 0, 2938808, 163349605168] [2] 58982400  
284592.eu6 284592eu4 [0, -1, 0, 11950888, -11097701712] [2] 29491200  

Rank

sage: E.rank()
 

The elliptic curves in class 284592.eu have rank \(0\).

Modular form 284592.2.a.eu

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{9} + 6q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.