# Properties

 Label 9792.bj Number of curves 4 Conductor 9792 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9792.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 9792.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9792.bj1 9792bx4 [0, 0, 0, -65100, -4417904] [2] 55296
9792.bj2 9792bx3 [0, 0, 0, -59340, -5562992] [2] 27648
9792.bj3 9792bx2 [0, 0, 0, -24780, 1501072] [2] 18432
9792.bj4 9792bx1 [0, 0, 0, -1740, 17296] [2] 9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9792.bj have rank $$0$$.

## Modular form9792.2.a.bj

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 LMFDB 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 LMFDB labels.