Properties

Label 254898de
Number of curves $6$
Conductor $254898$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("254898.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 254898de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
254898.de5 254898de1 [1, -1, 0, -8952530211, 325631283424789] [2] 424673280 \(\Gamma_0(N)\)-optimal
254898.de4 254898de2 [1, -1, 0, -11562685731, 120273121639957] [2, 2] 849346560  
254898.de6 254898de3 [1, -1, 0, 44596441629, 945935843912149] [2] 1698693120  
254898.de2 254898de4 [1, -1, 0, -109484301411, -13848343276727723] [2, 2] 1698693120  
254898.de3 254898de5 [1, -1, 0, -37292089851, -31838079298229555] [2] 3397386240  
254898.de1 254898de6 [1, -1, 0, -1748422363851, -889851231810145571] [2] 3397386240  

Rank

sage: E.rank()
 

The elliptic curves in class 254898de have rank \(1\).

Modular form 254898.2.a.de

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 2q^{5} - q^{8} - 2q^{10} + 4q^{11} + 2q^{13} + q^{16} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.