# Properties

 Label 382200eo Number of curves $4$ Conductor $382200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eo1")

sage: E.isogeny_class()

## Elliptic curves in class 382200eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.eo4 382200eo1 $$[0, -1, 0, -24908, -5362188]$$ $$-3631696/24375$$ $$-11470777500000000$$ $$[2]$$ $$2654208$$ $$1.7649$$ $$\Gamma_0(N)$$-optimal
382200.eo3 382200eo2 $$[0, -1, 0, -637408, -195237188]$$ $$15214885924/38025$$ $$71577651600000000$$ $$[2, 2]$$ $$5308416$$ $$2.1115$$
382200.eo2 382200eo3 $$[0, -1, 0, -882408, -31087188]$$ $$20183398562/11567205$$ $$43547843233440000000$$ $$[2]$$ $$10616832$$ $$2.4581$$
382200.eo1 382200eo4 $$[0, -1, 0, -10192408, -12521187188]$$ $$31103978031362/195$$ $$734129760000000$$ $$[2]$$ $$10616832$$ $$2.4581$$

## Rank

sage: E.rank()

The elliptic curves in class 382200eo have rank $$1$$.

## Complex multiplication

The elliptic curves in class 382200eo do not have complex multiplication.

## Modular form 382200.2.a.eo

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.