Properties

Label 221067h
Number of curves $4$
Conductor $221067$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.m4 221067h1 [1, -1, 1, -36823469, 86930004516] [2] 19906560 \(\Gamma_0(N)\)-optimal
221067.m3 221067h2 [1, -1, 1, -590912114, 5528967040248] [2, 2] 39813120  
221067.m1 221067h3 [1, -1, 1, -9454593479, 353846826376926] [2] 79626240  
221067.m2 221067h4 [1, -1, 1, -592649069, 5494828926678] [2] 79626240  

Rank

sage: E.rank()
 

The elliptic curves in class 221067h have rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.h

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

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.