Properties

Label 84150.fo
Number of curves 6
Conductor 84150
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("84150.fo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84150.fo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.fo1 84150fu6 [1, -1, 1, -65731505, 205112239247] [2] 9437184  
84150.fo2 84150fu4 [1, -1, 1, -4475255, 2599076747] [2, 2] 4718592  
84150.fo3 84150fu2 [1, -1, 1, -1662755, -792798253] [2, 2] 2359296  
84150.fo4 84150fu1 [1, -1, 1, -1644755, -811482253] [2] 1179648 \(\Gamma_0(N)\)-optimal
84150.fo5 84150fu3 [1, -1, 1, 861745, -2989113253] [2] 4718592  
84150.fo6 84150fu5 [1, -1, 1, 11780995, 17132164247] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 84150.fo have rank \(1\).

Modular form 84150.2.a.fo

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} + q^{11} - 6q^{13} + q^{16} + q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.