Properties

Label 162624hl
Number of curves $4$
Conductor $162624$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("hl1")
 
E.isogeny_class()
 

Elliptic curves in class 162624hl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.v4 162624hl1 \([0, -1, 0, 9156, -140490]\) \(748613312/505197\) \(-57279187361088\) \([2]\) \(491520\) \(1.3286\) \(\Gamma_0(N)\)-optimal
162624.v3 162624hl2 \([0, -1, 0, -39849, -1130391]\) \(964430272/480249\) \(3484837473030144\) \([2, 2]\) \(983040\) \(1.6752\)  
162624.v2 162624hl3 \([0, -1, 0, -344769, 77234049]\) \(78073482824/922383\) \(53544804347510784\) \([2]\) \(1966080\) \(2.0218\)  
162624.v1 162624hl4 \([0, -1, 0, -519009, -143632575]\) \(266344154504/237699\) \(13798548378058752\) \([2]\) \(1966080\) \(2.0218\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162624hl have rank \(0\).

Complex multiplication

The elliptic curves in class 162624hl do not have complex multiplication.

Modular form 162624.2.a.hl

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - q^{7} + q^{9} + 2 q^{13} + 2 q^{15} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.