Properties

Label 200277s
Number of curves 6
Conductor 200277
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("200277.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 200277s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
200277.s4 200277s1 [1, -1, 0, -88488, -10106181] [2] 819200 \(\Gamma_0(N)\)-optimal
200277.s3 200277s2 [1, -1, 0, -101493, -6930360] [2, 2] 1638400  
200277.s2 200277s3 [1, -1, 0, -738738, 239683455] [2, 2] 3276800  
200277.s6 200277s4 [1, -1, 0, 327672, -50447691] [2] 3276800  
200277.s1 200277s5 [1, -1, 0, -11753973, 15513408306] [2] 6553600  
200277.s5 200277s6 [1, -1, 0, 80577, 741595824] [2] 6553600  

Rank

sage: E.rank()
 

The elliptic curves in class 200277s have rank \(0\).

Modular form 200277.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 2q^{10} - q^{11} + 6q^{13} - q^{14} - q^{16} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.