Properties

Label 123210.br
Number of curves $4$
Conductor $123210$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 123210.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123210.br1 123210m4 \([1, -1, 0, -298014, -16294330]\) \(57960603/31250\) \(1578162278385843750\) \([2]\) \(2384640\) \(2.1830\)  
123210.br2 123210m2 \([1, -1, 0, -174804, 28173528]\) \(8527173507/200\) \(13854922608600\) \([2]\) \(794880\) \(1.6337\)  
123210.br3 123210m1 \([1, -1, 0, -10524, 475920]\) \(-1860867/320\) \(-22167876173760\) \([2]\) \(397440\) \(1.2871\) \(\Gamma_0(N)\)-optimal
123210.br4 123210m3 \([1, -1, 0, 71616, -2026612]\) \(804357/500\) \(-25250596454173500\) \([2]\) \(1192320\) \(1.8364\)  

Rank

sage: E.rank()
 

The elliptic curves in class 123210.br have rank \(0\).

Complex multiplication

The elliptic curves in class 123210.br do not have complex multiplication.

Modular form 123210.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 6 q^{11} + 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.