↑

Properties

Label 486720oj
Number of curves $2$
Conductor $486720$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("oj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 486720oj have rank \(0\).

Complex multiplication

The elliptic curves in class 486720oj do not have complex multiplication.

Modular form 486720.2.a.oj

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} - 4 q^{11} + 2 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 486720oj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.oj1 486720oj1 \([0, 0, 0, -354279432, -2284346023544]\) \(621217777580032/74733890625\) \(591609647907050889168000000\) \([2]\) \(187858944\) \(3.8678\) \(\Gamma_0(N)\)-optimal
486720.oj2 486720oj2 \([0, 0, 0, 510591588, -11697256256816]\) \(116227003261808/533935546875\) \(-67627989015437916000000000000\) \([2]\) \(375717888\) \(4.2144\)