↑

Properties

Label 320790j
Number of curves $2$
Conductor $320790$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 320790j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.j1 320790j1 \([1, 1, 0, -1580625827, 24186856979469]\) \(18093284246487294898042969/22310087184875520\) \(538511268820948620410880\) \([2]\) \(176947200\) \(3.8336\) \(\Gamma_0(N)\)-optimal
320790.j2 320790j2 \([1, 1, 0, -1567308707, 24614451058701]\) \(-17639806755131374412380249/635879957694262502400\) \(-15348596354562342055792665600\) \([2]\) \(353894400\) \(4.1802\)  

Rank

sage: E.rank()
 

The elliptic curves in class 320790j have rank \(0\).

Complex multiplication

The elliptic curves in class 320790j do not have complex multiplication.

Modular form 320790.2.a.j

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.