# Properties

 Label 433200g Number of curves $2$ Conductor $433200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("433200.g1")

sage: E.isogeny_class()

## Elliptic curves in class 433200g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
433200.g2 433200g1 [0, -1, 0, -341292408, -122842892688]  336199680 $$\Gamma_0(N)$$-optimal
433200.g1 433200g2 [0, -1, 0, -3853100408, -91823173388688]  672399360

## Rank

sage: E.rank()

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

## Modular form 433200.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} - 6q^{11} - 4q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 