Properties

Label 171941.q
Number of curves $4$
Conductor $171941$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 171941.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
171941.q1 171941q3 \([1, -1, 0, -316345871, 2165507025534]\) \(16798320881842096017/2132227789307\) \(444403990739271763908323\) \([2]\) \(30965760\) \(3.5594\)  
171941.q2 171941q4 \([1, -1, 0, -125491361, -518953130228]\) \(1048626554636928177/48569076788309\) \(10122882582944765789579501\) \([2]\) \(30965760\) \(3.5594\)  
171941.q3 171941q2 \([1, -1, 0, -21467056, 27694592547]\) \(5249244962308257/1448621666569\) \(301925175594804742544641\) \([2, 2]\) \(15482880\) \(3.2129\)  
171941.q4 171941q1 \([1, -1, 0, 3464389, 2827969304]\) \(22062729659823/29354283343\) \(-6118089600154947557527\) \([2]\) \(7741440\) \(2.8663\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 171941.q have rank \(1\).

Complex multiplication

The elliptic curves in class 171941.q do not have complex multiplication.

Modular form 171941.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2q^{5} - 3q^{8} - 3q^{9} + 2q^{10} + 6q^{13} - q^{16} - 2q^{17} - 3q^{18} - 8q^{19} + O(q^{20})\)  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.