# Properties

 Label 433200eg Number of curves $2$ Conductor $433200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("eg1")

sage: E.isogeny_class()

## Elliptic curves in class 433200eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.eg2 433200eg1 $$[0, -1, 0, -90408, 10803312]$$ $$-186169411/6480$$ $$-2844564480000000$$ $$[2]$$ $$2211840$$ $$1.7383$$ $$\Gamma_0(N)$$-optimal*
433200.eg1 433200eg2 $$[0, -1, 0, -1458408, 678387312]$$ $$781484460931/900$$ $$395078400000000$$ $$[2]$$ $$4423680$$ $$2.0849$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200eg1.

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 433200.2.a.eg

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{7} + q^{9} + 2 q^{13} + 6 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.