Properties

Label 236992.bo
Number of curves $4$
Conductor $236992$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bo1 236992bo4 \([0, 0, 0, -4187564, -3297549008]\) \(209267191953/55223\) \(2143023503310061568\) \([2]\) \(5406720\) \(2.5018\)  
236992.bo2 236992bo2 \([0, 0, 0, -294124, -37961040]\) \(72511713/25921\) \(1005908991349620736\) \([2, 2]\) \(2703360\) \(2.1553\)  
236992.bo3 236992bo1 \([0, 0, 0, -124844, 16547120]\) \(5545233/161\) \(6247881933848576\) \([2]\) \(1351680\) \(1.8087\) \(\Gamma_0(N)\)-optimal
236992.bo4 236992bo3 \([0, 0, 0, 890836, -266895312]\) \(2014698447/1958887\) \(-76017979489135624192\) \([2]\) \(5406720\) \(2.5018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236992.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 236992.bo do not have complex multiplication.

Modular form 236992.2.a.bo

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} - 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.