Properties

Label 158400kh
Number of curves 4
Conductor 158400
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("158400.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 158400kh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.y4 158400kh1 [0, 0, 0, 600, -155000] [2] 393216 \(\Gamma_0(N)\)-optimal
158400.y3 158400kh2 [0, 0, 0, -39900, -2990000] [2, 2] 786432  
158400.y2 158400kh3 [0, 0, 0, -93900, 6838000] [2] 1572864  
158400.y1 158400kh4 [0, 0, 0, -633900, -194258000] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 158400kh have rank \(0\).

Modular form 158400.2.a.y

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - q^{11} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.