Properties

Label 144150.br
Number of curves $4$
Conductor $144150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 144150.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144150.br1 144150di4 \([1, 0, 1, -15267191276, 726082642379198]\) \(28379906689597370652529/1357352437500\) \(18822738823368319335937500\) \([2]\) \(199065600\) \(4.3270\)  
144150.br2 144150di3 \([1, 0, 1, -952615776, 11384516815198]\) \(-6894246873502147249/47925198774000\) \(-664590473821588860843750000\) \([2]\) \(99532800\) \(3.9805\)  
144150.br3 144150di2 \([1, 0, 1, -204957776, 811579439198]\) \(68663623745397169/19216056254400\) \(266473760313798006975000000\) \([2]\) \(66355200\) \(3.7777\)  
144150.br4 144150di1 \([1, 0, 1, 33370224, 83249071198]\) \(296354077829711/387386634240\) \(-5371985372784384960000000\) \([2]\) \(33177600\) \(3.4312\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 144150.br have rank \(1\).

Complex multiplication

The elliptic curves in class 144150.br do not have complex multiplication.

Modular form 144150.2.a.br

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