Properties

Label 199920p
Number of curves 4
Conductor 199920
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("199920.hc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 199920p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
199920.hc4 199920p1 [0, 1, 0, 10960, 746388] [2] 786432 \(\Gamma_0(N)\)-optimal
199920.hc3 199920p2 [0, 1, 0, -87040, 8076788] [2, 2] 1572864  
199920.hc1 199920p3 [0, 1, 0, -1321840, 584481428] [4] 3145728  
199920.hc2 199920p4 [0, 1, 0, -420240, -97614252] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 199920p have rank \(0\).

Modular form 199920.2.a.hc

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.