# Properties

 Label 54080bf Number of curves 4 Conductor 54080 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54080.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 54080bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54080.cd3 54080bf1 [0, 0, 0, -1352, 17576] [2] 36864 $$\Gamma_0(N)$$-optimal
54080.cd2 54080bf2 [0, 0, 0, -4732, -105456] [2, 2] 73728
54080.cd4 54080bf3 [0, 0, 0, 8788, -597584] [2] 147456
54080.cd1 54080bf4 [0, 0, 0, -72332, -7487376] [2] 147456

## Rank

sage: E.rank()

The elliptic curves in class 54080bf have rank $$0$$.

## Modular form 54080.2.a.cd

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 3q^{9} + 4q^{11} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.