Properties

Label 98022q
Number of curves 6
Conductor 98022
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("98022.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 98022q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98022.n5 98022q1 [1, 1, 1, -32694, -2123853] [2] 460800 \(\Gamma_0(N)\)-optimal
98022.n4 98022q2 [1, 1, 1, -109574, 11468531] [2, 2] 921600  
98022.n6 98022q3 [1, 1, 1, 217166, 67145027] [2] 1843200  
98022.n2 98022q4 [1, 1, 1, -1666394, 827242211] [2, 2] 1843200  
98022.n3 98022q5 [1, 1, 1, -1579904, 917053427] [2] 3686400  
98022.n1 98022q6 [1, 1, 1, -26662004, 52978082915] [2] 3686400  

Rank

sage: E.rank()
 

The elliptic curves in class 98022q have rank \(1\).

Modular form 98022.2.a.n

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.