Properties

Label 227850.cy
Number of curves $6$
Conductor $227850$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("227850.cy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227850.cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227850.cy1 227850ga5 [1, 0, 1, -376712026, 2814216436448] [2] 37748736  
227850.cy2 227850ga3 [1, 0, 1, -23544526, 43970566448] [2, 2] 18874368  
227850.cy3 227850ga6 [1, 0, 1, -23177026, 45409696448] [2] 37748736  
227850.cy4 227850ga4 [1, 0, 1, -4532526, -2896169552] [2] 18874368  
227850.cy5 227850ga2 [1, 0, 1, -1494526, 664366448] [2, 2] 9437184  
227850.cy6 227850ga1 [1, 0, 1, 73474, 43438448] [2] 4718592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 227850.cy have rank \(0\).

Modular form 227850.2.a.cy

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 4q^{11} + q^{12} + 6q^{13} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.