# Properties

 Label 38720dn Number of curves 4 Conductor 38720 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38720.p1")

sage: E.isogeny_class()

## Elliptic curves in class 38720dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.p3 38720dn1 [0, 1, 0, -645, 4123] [2] 23040 $$\Gamma_0(N)$$-optimal
38720.p4 38720dn2 [0, 1, 0, 1775, 29775] [2] 46080
38720.p1 38720dn3 [0, 1, 0, -20005, -1095525] [2] 69120
38720.p2 38720dn4 [0, 1, 0, -17585, -1368017] [2] 138240

## Rank

sage: E.rank()

The elliptic curves in class 38720dn have rank $$0$$.

## Modular form 38720.2.a.p

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.