# Properties

 Label 54096bw Number of curves $6$ Conductor $54096$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54096.bi1")

sage: E.isogeny_class()

## Elliptic curves in class 54096bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54096.bi5 54096bw1 [0, -1, 0, 98768, 24436672] [2] 589824 $$\Gamma_0(N)$$-optimal
54096.bi4 54096bw2 [0, -1, 0, -904752, 283746240] [2, 2] 1179648
54096.bi3 54096bw3 [0, -1, 0, -3978032, -2777240640] [2, 2] 2359296
54096.bi2 54096bw4 [0, -1, 0, -13887792, 19924489152] [2] 2359296
54096.bi6 54096bw5 [0, -1, 0, 4912528, -13438800192] [4] 4718592
54096.bi1 54096bw6 [0, -1, 0, -62041072, -188068013888] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 54096bw have rank $$0$$.

## Modular form 54096.2.a.bi

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.