Properties

Label 221067y
Number of curves $4$
Conductor $221067$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.z3 221067y1 [1, -1, 0, -168273, -21544880] [2] 1474560 \(\Gamma_0(N)\)-optimal
221067.z2 221067y2 [1, -1, 0, -827118, 270323455] [2, 2] 2949120  
221067.z1 221067y3 [1, -1, 0, -12985803, 18014708344] [2] 5898240  
221067.z4 221067y4 [1, -1, 0, 790047, 1197605866] [2] 5898240  

Rank

sage: E.rank()
 

The elliptic curves in class 221067y have rank \(0\).

Complex multiplication

The elliptic curves in class 221067y do not have complex multiplication.

Modular form 221067.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 2q^{10} - 2q^{13} + q^{14} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.