# Properties

 Label 58800kg Number of curves $2$ Conductor $58800$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("kg1")

sage: E.isogeny_class()

## Elliptic curves in class 58800kg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.fh2 58800kg1 $$[0, 1, 0, 19192, -76812]$$ $$2595575/1512$$ $$-455386337280000$$ $$[]$$ $$248832$$ $$1.5021$$ $$\Gamma_0(N)$$-optimal
58800.fh1 58800kg2 $$[0, 1, 0, -274808, -58759212]$$ $$-7620530425/526848$$ $$-158676839301120000$$ $$[]$$ $$746496$$ $$2.0514$$

## Rank

sage: E.rank()

The elliptic curves in class 58800kg have rank $$1$$.

## Complex multiplication

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

## Modular form 58800.2.a.kg

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 6q^{11} + q^{13} - 3q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 