Properties

Label 4114.a
Number of curves 4
Conductor 4114
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4114.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4114.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4114.a1 4114b4 [1, 0, 1, -13676, 424224] [2] 12960  
4114.a2 4114b3 [1, 0, 1, -12466, 534576] [2] 6480  
4114.a3 4114b2 [1, 0, 1, -5206, -144960] [2] 4320  
4114.a4 4114b1 [1, 0, 1, -366, -1696] [2] 2160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4114.a have rank \(1\).

Modular form 4114.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + 4q^{7} - q^{8} + q^{9} - 2q^{12} - 2q^{13} - 4q^{14} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.