# Properties

 Label 9792v Number of curves 4 Conductor 9792 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9792.y1")

sage: E.isogeny_class()

## Elliptic curves in class 9792v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9792.y4 9792v1 [0, 0, 0, -1740, -17296]  9216 $$\Gamma_0(N)$$-optimal
9792.y3 9792v2 [0, 0, 0, -24780, -1501072]  18432
9792.y2 9792v3 [0, 0, 0, -59340, 5562992]  27648
9792.y1 9792v4 [0, 0, 0, -65100, 4417904]  55296

## Rank

sage: E.rank()

The elliptic curves in class 9792v have rank $$1$$.

## Modular form9792.2.a.y

sage: E.q_eigenform(10)

$$q - 4q^{7} + 6q^{11} - 2q^{13} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 