# Properties

 Label 116928.br Number of curves $6$ Conductor $116928$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("116928.br1")

sage: E.isogeny_class()

## Elliptic curves in class 116928.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116928.br1 116928ck4 [0, 0, 0, -117863436, -492511936016] [2] 6291456
116928.br2 116928ck6 [0, 0, 0, -24462156, 37856255344] [2] 12582912
116928.br3 116928ck3 [0, 0, 0, -7507596, -7385292560] [2, 2] 6291456
116928.br4 116928ck2 [0, 0, 0, -7366476, -7695474320] [2, 2] 3145728
116928.br5 116928ck1 [0, 0, 0, -451596, -125063696] [2] 1572864 $$\Gamma_0(N)$$-optimal
116928.br6 116928ck5 [0, 0, 0, 7189044, -32775207824] [2] 12582912

## Rank

sage: E.rank()

The elliptic curves in class 116928.br have rank $$0$$.

## Modular form 116928.2.a.br

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} + 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.