# Properties

 Label 433200gt Number of curves $2$ Conductor $433200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("433200.gt1")

sage: E.isogeny_class()

## Elliptic curves in class 433200gt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
433200.gt2 433200gt1 [0, 1, 0, -584408, -237976812] [2] 5898240 $$\Gamma_0(N)$$-optimal*
433200.gt1 433200gt2 [0, 1, 0, -10312408, -12748184812] [2] 11796480 $$\Gamma_0(N)$$-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200gt1.

## Rank

sage: E.rank()

The elliptic curves in class 433200gt have rank $$1$$.

## Modular form 433200.2.a.gt

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.