# Properties

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

# Related objects

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)

$$q + q^{3} + 2 q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{15} + q^{17} - 4 q^{19} + O(q^{20})$$

## 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.