↑

Properties

Label 28050bx
Number of curves $2$
Conductor $28050$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 28050bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.ci1 28050bx1 \([1, 1, 1, -212588, 37638281]\) \(68001744211490809/1022422500\) \(15975351562500\) \([2]\) \(193536\) \(1.6701\) \(\Gamma_0(N)\)-optimal
28050.ci2 28050bx2 \([1, 1, 1, -206338, 39963281]\) \(-62178675647294809/8362782148050\) \(-130668471063281250\) \([2]\) \(387072\) \(2.0167\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28050bx have rank \(0\).

Complex multiplication

The elliptic curves in class 28050bx do not have complex multiplication.

Modular form 28050.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{11} - q^{12} - 4 q^{13} + q^{16} - q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.