Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 4114.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4114.a1 4114b4 \([1, 0, 1, -13676, 424224]\) \(159661140625/48275138\) \(85522351750418\) \([2]\) \(12960\) \(1.3784\)  
4114.a2 4114b3 \([1, 0, 1, -12466, 534576]\) \(120920208625/19652\) \(34814716772\) \([2]\) \(6480\) \(1.0319\)  
4114.a3 4114b2 \([1, 0, 1, -5206, -144960]\) \(8805624625/2312\) \(4095849032\) \([2]\) \(4320\) \(0.82913\)  
4114.a4 4114b1 \([1, 0, 1, -366, -1696]\) \(3048625/1088\) \(1927458368\) \([2]\) \(2160\) \(0.48256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 4114.a do not have complex multiplication.

Modular form 4114.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.