Properties

Label 23805t
Number of curves 8
Conductor 23805
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("23805.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23805t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23805.s7 23805t1 [1, -1, 0, -99, 61240] [2] 25344 \(\Gamma_0(N)\)-optimal
23805.s6 23805t2 [1, -1, 0, -23904, 1408603] [2, 2] 50688  
23805.s5 23805t3 [1, -1, 0, -47709, -1843160] [2, 2] 101376  
23805.s4 23805t4 [1, -1, 0, -380979, 90605938] [2] 101376  
23805.s8 23805t5 [1, -1, 0, 166536, -13969427] [2] 202752  
23805.s2 23805t6 [1, -1, 0, -642834, -198115385] [2, 2] 202752  
23805.s3 23805t7 [1, -1, 0, -523809, -273839090] [2] 405504  
23805.s1 23805t8 [1, -1, 0, -10283859, -12690955580] [2] 405504  

Rank

sage: E.rank()
 

The elliptic curves in class 23805t have rank \(0\).

Modular form 23805.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + q^{5} - 3q^{8} + q^{10} - 4q^{11} - 2q^{13} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.