# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("bj1")

E.isogeny_class()

## Elliptic curves in class 9792.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9792.bj1 9792bx4 $$[0, 0, 0, -65100, -4417904]$$ $$159661140625/48275138$$ $$9225522538610688$$ $$[2]$$ $$55296$$ $$1.7685$$
9792.bj2 9792bx3 $$[0, 0, 0, -59340, -5562992]$$ $$120920208625/19652$$ $$3755555684352$$ $$[2]$$ $$27648$$ $$1.4219$$
9792.bj3 9792bx2 $$[0, 0, 0, -24780, 1501072]$$ $$8805624625/2312$$ $$441830080512$$ $$[2]$$ $$18432$$ $$1.2192$$
9792.bj4 9792bx1 $$[0, 0, 0, -1740, 17296]$$ $$3048625/1088$$ $$207920037888$$ $$[2]$$ $$9216$$ $$0.87263$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 9792.bj do not have complex multiplication.

## Modular form9792.2.a.bj

sage: E.q_eigenform(10)

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

## 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.