Properties

Label 388080dj
Number of curves 4
Conductor 388080
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("388080.dj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 388080dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
388080.dj3 388080dj1 [0, 0, 0, -395283, -1861486382] [2] 15925248 \(\Gamma_0(N)\)-optimal
388080.dj2 388080dj2 [0, 0, 0, -25232403, -48351607598] [2] 31850496  
388080.dj4 388080dj3 [0, 0, 0, 3556077, 50143943122] [2] 47775744  
388080.dj1 388080dj4 [0, 0, 0, -184274643, 935540391058] [2] 95551488  

Rank

sage: E.rank()
 

The elliptic curves in class 388080dj have rank \(0\).

Modular form 388080.2.a.dj

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.