# Properties

 Label 81600cn Number of curves 6 Conductor 81600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("81600.hv1")

sage: E.isogeny_class()

## Elliptic curves in class 81600cn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
81600.hv5 81600cn1 [0, 1, 0, -54433, 4515263] [2] 393216 $$\Gamma_0(N)$$-optimal
81600.hv4 81600cn2 [0, 1, 0, -182433, -24796737] [2, 2] 786432
81600.hv6 81600cn3 [0, 1, 0, 361567, -143932737] [2] 1572864
81600.hv2 81600cn4 [0, 1, 0, -2774433, -1779580737] [2, 2] 1572864
81600.hv3 81600cn5 [0, 1, 0, -2630433, -1972396737] [2] 3145728
81600.hv1 81600cn6 [0, 1, 0, -44390433, -113851468737] [2] 3145728

## Rank

sage: E.rank()

The elliptic curves in class 81600cn have rank $$0$$.

## Modular form 81600.2.a.hv

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.