Properties

Label 39600dl
Number of curves 4
Conductor 39600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("39600.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39600dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.f4 39600dl1 [0, 0, 0, -10200, 388375] [2] 82944 \(\Gamma_0(N)\)-optimal
39600.f3 39600dl2 [0, 0, 0, -22575, -737750] [2] 165888  
39600.f2 39600dl3 [0, 0, 0, -100200, -12054125] [2] 248832  
39600.f1 39600dl4 [0, 0, 0, -1597575, -777212750] [2] 497664  

Rank

sage: E.rank()
 

The elliptic curves in class 39600dl have rank \(1\).

Modular form 39600.2.a.f

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - q^{11} + 4q^{13} + 4q^{19} + O(q^{20}) \)

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.