# Properties

 Label 28050.cx Number of curves $8$ Conductor $28050$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

## Elliptic curves in class 28050.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.cx1 28050cm8 $$[1, 1, 1, -5030912063, -137348787904219]$$ $$901247067798311192691198986281/552431869440$$ $$8631747960000000$$ $$[2]$$ $$15925248$$ $$3.7655$$
28050.cx2 28050cm7 $$[1, 1, 1, -316544063, -2115881920219]$$ $$224494757451893010998773801/6152490825146276160000$$ $$96132669142910565000000000$$ $$[2]$$ $$15925248$$ $$3.7655$$
28050.cx3 28050cm6 $$[1, 1, 1, -314432063, -2146172224219]$$ $$220031146443748723000125481/172266701724057600$$ $$2691667214438400000000$$ $$[2, 2]$$ $$7962624$$ $$3.4189$$
28050.cx4 28050cm5 $$[1, 1, 1, -62122688, -188349461719]$$ $$1696892787277117093383481/1440538624914939000$$ $$22508416014295921875000$$ $$[2]$$ $$5308416$$ $$3.2162$$
28050.cx5 28050cm4 $$[1, 1, 1, -40684688, 98799642281]$$ $$476646772170172569823801/5862293314453125000$$ $$91598333038330078125000$$ $$[2]$$ $$5308416$$ $$3.2162$$
28050.cx6 28050cm3 $$[1, 1, 1, -19520063, -34012480219]$$ $$-52643812360427830814761/1504091705903677440$$ $$-23501432904744960000000$$ $$[2]$$ $$3981312$$ $$3.0724$$
28050.cx7 28050cm2 $$[1, 1, 1, -4747688, -1536461719]$$ $$757443433548897303481/373234243041000000$$ $$5831785047515625000000$$ $$[2, 2]$$ $$2654208$$ $$2.8696$$
28050.cx8 28050cm1 $$[1, 1, 1, 1084312, -183437719]$$ $$9023321954633914439/6156756739584000$$ $$-96199324056000000000$$ $$[2]$$ $$1327104$$ $$2.5231$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 28050.cx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 28050.cx do not have complex multiplication.

## Modular form 28050.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{11} - q^{12} - 2 q^{13} + 4 q^{14} + q^{16} + q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.