# Properties

 Label 58800gg Number of curves $2$ Conductor $58800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gg1")

sage: E.isogeny_class()

## Elliptic curves in class 58800gg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.d2 58800gg1 $$[0, -1, 0, 479792, -10561088]$$ $$2595575/1512$$ $$-7115411520000000000$$ $$[]$$ $$1244160$$ $$2.3068$$ $$\Gamma_0(N)$$-optimal
58800.d1 58800gg2 $$[0, -1, 0, -6870208, -7331161088]$$ $$-7620530425/526848$$ $$-2479325614080000000000$$ $$[]$$ $$3732480$$ $$2.8561$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.gg

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.