Properties

Label 4410t
Number of curves 6
Conductor 4410
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4410.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.l6 4410t1 [1, -1, 0, 4401, -158355] [2] 12288 \(\Gamma_0(N)\)-optimal
4410.l5 4410t2 [1, -1, 0, -30879, -1618947] [2, 2] 24576  
4410.l2 4410t3 [1, -1, 0, -463059, -121159935] [2, 2] 49152  
4410.l4 4410t4 [1, -1, 0, -163179, 24020793] [2] 49152  
4410.l1 4410t5 [1, -1, 0, -7408809, -7760095785] [2] 98304  
4410.l3 4410t6 [1, -1, 0, -432189, -138033477] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 4410t have rank \(0\).

Modular form 4410.2.a.l

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.