# Properties

 Label 51870o Number of curves 4 Conductor 51870 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("51870.n1")
sage: E.isogeny_class()

## Elliptic curves in class 51870o

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
51870.n4 51870o1 [1, 1, 0, 838, 1991316] 2 368640 $$\Gamma_0(N)$$-optimal
51870.n3 51870o2 [1, 1, 0, -232442, 42255444] 4 737280
51870.n2 51870o3 [1, 1, 0, -497042, -72104676] 2 1474560
51870.n1 51870o4 [1, 1, 0, -3700322, 2738185356] 2 1474560

## Rank

sage: E.rank()

The elliptic curves in class 51870o have rank $$0$$.

## Modular form None

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} - q^{18} - q^{19} + O(q^{20})$$

## 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.