Properties

Label 4410.f
Number of curves 8
Conductor 4410
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4410.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.f1 4410h7 [1, -1, 0, -2844900, 1162675786] [2] 221184  
4410.f2 4410h4 [1, -1, 0, -2540610, 1559308540] [2] 73728  
4410.f3 4410h6 [1, -1, 0, -1191150, -486774464] [2, 2] 110592  
4410.f4 4410h3 [1, -1, 0, -1182330, -494534300] [2] 55296  
4410.f5 4410h2 [1, -1, 0, -159210, 24258100] [2, 2] 36864  
4410.f6 4410h5 [1, -1, 0, -35730, 60832876] [2] 73728  
4410.f7 4410h1 [1, -1, 0, -18090, -325004] [2] 18432 \(\Gamma_0(N)\)-optimal
4410.f8 4410h8 [1, -1, 0, 321480, -1639701050] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 4410.f have rank \(1\).

Modular form 4410.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2q^{13} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.