Properties

Label 144144br
Number of curves $4$
Conductor $144144$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 144144br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144144.dx4 144144br1 \([0, 0, 0, -2259, -348462]\) \(-426957777/17320303\) \(-51718147633152\) \([2]\) \(311296\) \(1.3115\) \(\Gamma_0(N)\)-optimal
144144.dx3 144144br2 \([0, 0, 0, -89379, -10227870]\) \(26444947540257/169338169\) \(505641063223296\) \([2, 2]\) \(622592\) \(1.6581\)  
144144.dx2 144144br3 \([0, 0, 0, -144819, 3975858]\) \(112489728522417/62811265517\) \(187553433853513728\) \([2]\) \(1245184\) \(2.0047\)  
144144.dx1 144144br4 \([0, 0, 0, -1427859, -656713710]\) \(107818231938348177/4463459\) \(13327817158656\) \([2]\) \(1245184\) \(2.0047\)  

Rank

sage: E.rank()
 

The elliptic curves in class 144144br have rank \(1\).

Complex multiplication

The elliptic curves in class 144144br do not have complex multiplication.

Modular form 144144.2.a.br

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} + q^{11} - q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.