# Properties

 Label 277200hx Number of curves $4$ Conductor $277200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hx1")

sage: E.isogeny_class()

## Elliptic curves in class 277200hx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.hx3 277200hx1 $$[0, 0, 0, -598800, 180991375]$$ $$-130287139815424/2250652635$$ $$-410181442728750000$$ $$[2]$$ $$3981312$$ $$2.1776$$ $$\Gamma_0(N)$$-optimal
277200.hx2 277200hx2 $$[0, 0, 0, -9620175, 11484774250]$$ $$33766427105425744/9823275$$ $$28644669900000000$$ $$[2]$$ $$7962624$$ $$2.5241$$
277200.hx4 277200hx3 $$[0, 0, 0, 2317200, 867344875]$$ $$7549996227362816/6152409907875$$ $$-1121276705710218750000$$ $$[2]$$ $$11943936$$ $$2.7269$$
277200.hx1 277200hx4 $$[0, 0, 0, -11159175, 7565103250]$$ $$52702650535889104/22020583921875$$ $$64212022716187500000000$$ $$[2]$$ $$23887872$$ $$3.0734$$

## Rank

sage: E.rank()

The elliptic curves in class 277200hx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 277200hx do not have complex multiplication.

## Modular form 277200.2.a.hx

sage: E.q_eigenform(10)

$$q + q^{7} - q^{11} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.