Properties

Label 92400gz
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("gz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.hi2 92400gz1 [0, 1, 0, -3576133, -3049482637] [] 5760000 \(\Gamma_0(N)\)-optimal
92400.hi1 92400gz2 [0, 1, 0, -10716133, 255264377363] [] 28800000  

Rank

sage: E.rank()
 

The elliptic curves in class 92400gz have rank \(0\).

Complex multiplication

The elliptic curves in class 92400gz do not have complex multiplication.

Modular form 92400.2.a.gz

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} + q^{9} - q^{11} + 6q^{13} + 7q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.