# Properties

 Label 58800gi Number of curves $4$ Conductor $58800$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gi1")

sage: E.isogeny_class()

## Elliptic curves in class 58800gi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.c2 58800gi1 $$[0, -1, 0, -75133, 7931512]$$ $$1594753024/4725$$ $$138972881250000$$ $$$$ $$331776$$ $$1.5836$$ $$\Gamma_0(N)$$-optimal
58800.c3 58800gi2 $$[0, -1, 0, -44508, 14424012]$$ $$-20720464/178605$$ $$-84050798580000000$$ $$$$ $$663552$$ $$1.9301$$
58800.c1 58800gi3 $$[0, -1, 0, -369133, -79606988]$$ $$189123395584/16078125$$ $$472893832031250000$$ $$$$ $$995328$$ $$2.1329$$
58800.c4 58800gi4 $$[0, -1, 0, 396492, -367481988]$$ $$14647977776/132355125$$ $$-62285792404500000000$$ $$$$ $$1990656$$ $$2.4795$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.gi

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} - 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 