# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gh1")

sage: E.isogeny_class()

## Elliptic curves in class 58800gh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.a2 58800gh1 $$[0, -1, 0, -28408, -1820048]$$ $$505318200625/4251528$$ $$21332466892800$$ $$[]$$ $$207360$$ $$1.3831$$ $$\Gamma_0(N)$$-optimal
58800.a1 58800gh2 $$[0, -1, 0, -2296408, -1338669968]$$ $$266916252066900625/162$$ $$812851200$$ $$[]$$ $$622080$$ $$1.9324$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.gh

sage: E.q_eigenform(10)

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

## 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.