# Properties

 Label 44880br Number of curves $8$ Conductor $44880$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 44880br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44880.bh8 44880br1 $$[0, -1, 0, 693960, 93920112]$$ $$9023321954633914439/6156756739584000$$ $$-25218075605336064000$$ $$[2]$$ $$1327104$$ $$2.4115$$ $$\Gamma_0(N)$$-optimal
44880.bh7 44880br2 $$[0, -1, 0, -3038520, 786668400]$$ $$757443433548897303481/373234243041000000$$ $$1528767459495936000000$$ $$[2, 2]$$ $$2654208$$ $$2.7581$$
44880.bh6 44880br3 $$[0, -1, 0, -12492840, 17414389872]$$ $$-52643812360427830814761/1504091705903677440$$ $$-6160759627381462794240$$ $$[2]$$ $$3981312$$ $$2.9608$$
44880.bh5 44880br4 $$[0, -1, 0, -26038200, -50585416848]$$ $$476646772170172569823801/5862293314453125000$$ $$24011953416000000000000$$ $$[2]$$ $$5308416$$ $$3.1046$$
44880.bh4 44880br5 $$[0, -1, 0, -39758520, 96434924400]$$ $$1696892787277117093383481/1440538624914939000$$ $$5900446207651590144000$$ $$[2]$$ $$5308416$$ $$3.1046$$
44880.bh3 44880br6 $$[0, -1, 0, -201236520, 1098840178800]$$ $$220031146443748723000125481/172266701724057600$$ $$705604410261739929600$$ $$[2, 2]$$ $$7962624$$ $$3.3074$$
44880.bh2 44880br7 $$[0, -1, 0, -202588200, 1083331543152]$$ $$224494757451893010998773801/6152490825146276160000$$ $$25200602419799147151360000$$ $$[2]$$ $$15925248$$ $$3.6539$$
44880.bh1 44880br8 $$[0, -1, 0, -3219783720, 70322579406960]$$ $$901247067798311192691198986281/552431869440$$ $$2262760937226240$$ $$[2]$$ $$15925248$$ $$3.6539$$

## Rank

sage: E.rank()

The elliptic curves in class 44880br have rank $$1$$.

## Complex multiplication

The elliptic curves in class 44880br do not have complex multiplication.

## Modular form 44880.2.a.br

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.