# Properties

 Label 433200id Number of curves $4$ Conductor $433200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("id1")

sage: E.isogeny_class()

## Elliptic curves in class 433200id

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.id3 433200id1 $$[0, 1, 0, -4479408, 3625711188]$$ $$3301293169/22800$$ $$68649349555200000000$$ $$[2]$$ $$13271040$$ $$2.6399$$ $$\Gamma_0(N)$$-optimal
433200.id2 433200id2 $$[0, 1, 0, -7367408, -1624672812]$$ $$14688124849/8122500$$ $$24456330779040000000000$$ $$[2, 2]$$ $$26542080$$ $$2.9864$$
433200.id4 433200id3 $$[0, 1, 0, 28732592, -12815672812]$$ $$871257511151/527800050$$ $$-1589172374022019200000000$$ $$[2]$$ $$53084160$$ $$3.3330$$
433200.id1 433200id4 $$[0, 1, 0, -89675408, -326412040812]$$ $$26487576322129/44531250$$ $$134080760850000000000000$$ $$[2]$$ $$53084160$$ $$3.3330$$

## Rank

sage: E.rank()

The elliptic curves in class 433200id have rank $$0$$.

## Complex multiplication

The elliptic curves in class 433200id do not have complex multiplication.

## Modular form 433200.2.a.id

sage: E.q_eigenform(10)

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

## 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.