# Properties

 Label 162624.hy Number of curves 6 Conductor 162624 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162624.hy1")

sage: E.isogeny_class()

## Elliptic curves in class 162624.hy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162624.hy1 162624gh5 [0, 1, 0, -34995297, 79670741247] [2] 9830400
162624.hy2 162624gh3 [0, 1, 0, -2199457, 1229651135] [2, 2] 4915200
162624.hy3 162624gh2 [0, 1, 0, -302177, -35834625] [2, 2] 2457600
162624.hy4 162624gh1 [0, 1, 0, -263457, -52120257] [2] 1228800 $$\Gamma_0(N)$$-optimal
162624.hy5 162624gh6 [0, 1, 0, 239903, 3810006143] [2] 9830400
162624.hy6 162624gh4 [0, 1, 0, 975583, -258420417] [2] 4915200

## Rank

sage: E.rank()

The elliptic curves in class 162624.hy have rank $$1$$.

## Modular form 162624.2.a.hy

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.