# Properties

 Label 38720bu Number of curves 4 Conductor 38720 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38720.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 38720bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.bm3 38720bu1 [0, 0, 0, -968, 10648]  20480 $$\Gamma_0(N)$$-optimal
38720.bm2 38720bu2 [0, 0, 0, -3388, -63888] [2, 2] 40960
38720.bm4 38720bu3 [0, 0, 0, 6292, -362032]  81920
38720.bm1 38720bu4 [0, 0, 0, -51788, -4536048]  81920

## Rank

sage: E.rank()

The elliptic curves in class 38720bu have rank $$1$$.

## Modular form 38720.2.a.bm

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 3q^{9} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 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. 