# Properties

 Label 58800.x Number of curves $4$ Conductor $58800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.x1 58800hf4 $$[0, -1, 0, -16229208, 25088316912]$$ $$502270291349/1889568$$ $$1778446285056000000000$$ $$$$ $$3456000$$ $$2.9368$$
58800.x2 58800hf2 $$[0, -1, 0, -1039208, -407363088]$$ $$131872229/18$$ $$16941456000000000$$ $$$$ $$691200$$ $$2.1321$$
58800.x3 58800hf3 $$[0, -1, 0, -549208, 752956912]$$ $$-19465109/248832$$ $$-234198687744000000000$$ $$$$ $$1728000$$ $$2.5903$$
58800.x4 58800hf1 $$[0, -1, 0, -59208, -7523088]$$ $$-24389/12$$ $$-11294304000000000$$ $$$$ $$345600$$ $$1.7855$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58800.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 58800.x do not have complex multiplication.

## Modular form 58800.2.a.x

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 2q^{11} - 6q^{13} - 2q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 