# Properties

 Label 110466bj Number of curves 6 Conductor 110466 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("110466.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 110466bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110466.bu5 110466bj1 [1, -1, 1, -110534, 13145685] [2] 884736 $$\Gamma_0(N)$$-optimal
110466.bu4 110466bj2 [1, -1, 1, -370454, -71484267] [2, 2] 1769472
110466.bu6 110466bj3 [1, -1, 1, 734206, -417021915] [2] 3538944
110466.bu2 110466bj4 [1, -1, 1, -5633834, -5145382587] [2, 2] 3538944
110466.bu3 110466bj5 [1, -1, 1, -5341424, -5703534795] [2] 7077888
110466.bu1 110466bj6 [1, -1, 1, -90140324, -329379883419] [2] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 110466bj have rank $$0$$.

## Modular form 110466.2.a.bu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{5} + q^{8} + 2q^{10} + 4q^{11} + 2q^{13} + q^{16} - q^{17} + O(q^{20})$$

## 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.