↑

Properties

Label 483600.hk
Number of curves $4$
Conductor $483600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("hk1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 483600.hk have rank \(1\).

Complex multiplication

The elliptic curves in class 483600.hk do not have complex multiplication.

Modular form 483600.2.a.hk

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{7} + q^{9} - 4 q^{11} + q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 483600.hk

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
483600.hk1 483600hk3 \([0, 1, 0, -92851408, 344343447188]\) \(1383277217333832812809/27202500\) \(1740960000000000\) \([2]\) \(28311552\) \(2.9095\) \(\Gamma_0(N)\)-optimal*
483600.hk2 483600hk2 \([0, 1, 0, -5803408, 5378535188]\) \(337748263783145929/47358464400\) \(3030941721600000000\) \([2, 2]\) \(14155776\) \(2.5630\) \(\Gamma_0(N)\)-optimal*
483600.hk3 483600hk4 \([0, 1, 0, -5283408, 6382135188]\) \(-254850956966062729/127607200177860\) \(-8166860811383040000000\) \([4]\) \(28311552\) \(2.9095\)  
483600.hk4 483600hk1 \([0, 1, 0, -395408, 67879188]\) \(106827039259849/30599112960\) \(1958343229440000000\) \([2]\) \(7077888\) \(2.2164\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 483600.hk1.