Properties

Label 19600co
Number of curves 4
Conductor 19600
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("19600.dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.dm3 19600co1 [0, -1, 0, -1633, 18012] [2] 17280 \(\Gamma_0(N)\)-optimal
19600.dm4 19600co2 [0, -1, 0, 4492, 116012] [2] 34560  
19600.dm1 19600co3 [0, -1, 0, -50633, -4367488] [2] 51840  
19600.dm2 19600co4 [0, -1, 0, -44508, -5469988] [2] 103680  

Rank

sage: E.rank()
 

The elliptic curves in class 19600co have rank \(1\).

Modular form 19600.2.a.dm

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

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 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.