Properties

Label 9800ba
Number of curves 4
Conductor 9800
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9800.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9800ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9800.x3 9800ba1 [0, 0, 0, -2450, -42875] [2] 6912 \(\Gamma_0(N)\)-optimal
9800.x2 9800ba2 [0, 0, 0, -8575, 257250] [2, 2] 13824  
9800.x1 9800ba3 [0, 0, 0, -131075, 18264750] [2] 27648  
9800.x4 9800ba4 [0, 0, 0, 15925, 1457750] [2] 27648  

Rank

sage: E.rank()
 

The elliptic curves in class 9800ba have rank \(1\).

Modular form 9800.2.a.x

sage: E.q_eigenform(10)
 
\( q - 3q^{9} + 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.