Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 221067.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.m1 221067h3 \([1, -1, 1, -9454593479, 353846826376926]\) \(72371679832051361738355457/1627857\) \(2102325173612433\) \([2]\) \(79626240\) \(3.8853\)  
221067.m2 221067h4 \([1, -1, 1, -592649069, 5494828926678]\) \(17825137625614555960417/216318148151991039\) \(279367959451692970443529791\) \([2]\) \(79626240\) \(3.8853\)  
221067.m3 221067h2 \([1, -1, 1, -590912114, 5528967040248]\) \(17668869054438249282097/2649918412449\) \(3422284750141214346081\) \([2, 2]\) \(39813120\) \(3.5387\)  
221067.m4 221067h1 \([1, -1, 1, -36823469, 86930004516]\) \(-4275768267198290017/52843101620463\) \(-68245173125439959449647\) \([2]\) \(19906560\) \(3.1922\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 221067.2.a.m

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.