Properties

Label 38829f
Number of curves $6$
Conductor $38829$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 38829f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38829.h6 38829f1 \([1, 1, 0, 1811, 7288]\) \(103823/63\) \(-398245872087\) \([2]\) \(40320\) \(0.91508\) \(\Gamma_0(N)\)-optimal
38829.h5 38829f2 \([1, 1, 0, -7434, 49815]\) \(7189057/3969\) \(25089489941481\) \([2, 2]\) \(80640\) \(1.2617\)  
38829.h3 38829f3 \([1, 1, 0, -72149, -7444182]\) \(6570725617/45927\) \(290321240751423\) \([2]\) \(161280\) \(1.6082\)  
38829.h2 38829f4 \([1, 1, 0, -90639, 10450440]\) \(13027640977/21609\) \(136598334125841\) \([2, 2]\) \(161280\) \(1.6082\)  
38829.h4 38829f5 \([1, 1, 0, -62904, 17001447]\) \(-4354703137/17294403\) \(-109324200078714747\) \([2]\) \(322560\) \(1.9548\)  
38829.h1 38829f6 \([1, 1, 0, -1449654, 671203533]\) \(53297461115137/147\) \(929240368203\) \([2]\) \(322560\) \(1.9548\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38829f have rank \(1\).

Complex multiplication

The elliptic curves in class 38829f do not have complex multiplication.

Modular form 38829.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.