Properties

Label 24563.g
Number of curves $4$
Conductor $24563$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24563.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24563.g1 24563g4 \([1, -1, 0, -6456038, -6311586979]\) \(16798320881842096017/2132227789307\) \(3777371594652498227\) \([2]\) \(645120\) \(2.5865\)  
24563.g2 24563g3 \([1, -1, 0, -2561048, 1513714615]\) \(1048626554636928177/48569076788309\) \(86043082244173480349\) \([2]\) \(645120\) \(2.5865\)  
24563.g3 24563g2 \([1, -1, 0, -438103, -80617080]\) \(5249244962308257/1448621666569\) \(2566321648248644209\) \([2, 2]\) \(322560\) \(2.2399\)  
24563.g4 24563g1 \([1, -1, 0, 70702, -8265009]\) \(22062729659823/29354283343\) \(-52002903553408423\) \([2]\) \(161280\) \(1.8933\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24563.g have rank \(1\).

Complex multiplication

The elliptic curves in class 24563.g do not have complex multiplication.

Modular form 24563.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 3q^{9} - 2q^{10} - 6q^{13} + q^{14} - q^{16} + 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.