# Properties

 Label 52800ch Number of curves $4$ Conductor $52800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ch1")

sage: E.isogeny_class()

## Elliptic curves in class 52800ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52800.et4 52800ch1 $$[0, 1, 0, 21867, -4565637]$$ $$72268906496/606436875$$ $$-9702990000000000$$ $$[2]$$ $$221184$$ $$1.7490$$ $$\Gamma_0(N)$$-optimal
52800.et3 52800ch2 $$[0, 1, 0, -315633, -62953137]$$ $$13584145739344/1195803675$$ $$306125740800000000$$ $$[2]$$ $$442368$$ $$2.0955$$
52800.et2 52800ch3 $$[0, 1, 0, -1562133, -752609637]$$ $$-26348629355659264/24169921875$$ $$-386718750000000000$$ $$[2]$$ $$663552$$ $$2.2983$$
52800.et1 52800ch4 $$[0, 1, 0, -24999633, -48119797137]$$ $$6749703004355978704/5671875$$ $$1452000000000000$$ $$[2]$$ $$1327104$$ $$2.6448$$

## Rank

sage: E.rank()

The elliptic curves in class 52800ch have rank $$0$$.

## Complex multiplication

The elliptic curves in class 52800ch do not have complex multiplication.

## Modular form 52800.2.a.ch

sage: E.q_eigenform(10)

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

## 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.