Properties

Label 22848bn
Number of curves $6$
Conductor $22848$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cr5 22848bn1 \([0, 1, 0, -4495617, 3662779743]\) \(38331145780597164097/55468445663232\) \(14540720219942289408\) \([2]\) \(737280\) \(2.5791\) \(\Gamma_0(N)\)-optimal
22848.cr4 22848bn2 \([0, 1, 0, -5806337, 1351456095]\) \(82582985847542515777/44772582831427584\) \(11736863953761752580096\) \([2, 2]\) \(1474560\) \(2.9257\)  
22848.cr6 22848bn3 \([0, 1, 0, 22394623, 10652132703]\) \(4738217997934888496063/2928751705237796928\) \(-767754687017857037893632\) \([2]\) \(2949120\) \(3.2723\)  
22848.cr2 22848bn4 \([0, 1, 0, -54978817, -155852962465]\) \(70108386184777836280897/552468975892674624\) \(144826427216409296633856\) \([2, 2]\) \(2949120\) \(3.2723\)  
22848.cr3 22848bn5 \([0, 1, 0, -18726657, -358277773473]\) \(-2770540998624539614657/209924951154647363208\) \(-55030566395483878380797952\) \([4]\) \(5898240\) \(3.6189\)  
22848.cr1 22848bn6 \([0, 1, 0, -877990657, -10013724179617]\) \(285531136548675601769470657/17941034271597192\) \(4703134488093574299648\) \([2]\) \(5898240\) \(3.6189\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22848bn have rank \(0\).

Complex multiplication

The elliptic curves in class 22848bn do not have complex multiplication.

Modular form 22848.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{15} + q^{17} - 4 q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.