# Properties

 Label 56784bk Number of curves 6 Conductor 56784 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("56784.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 56784bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
56784.bh6 56784bk1 [0, -1, 0, 2648, 10672] [2] 73728 $$\Gamma_0(N)$$-optimal
56784.bh5 56784bk2 [0, -1, 0, -10872, 97200] [2, 2] 147456
56784.bh3 56784bk3 [0, -1, 0, -105512, -13076688] [2] 294912
56784.bh2 56784bk4 [0, -1, 0, -132552, 18592560] [2, 2] 294912
56784.bh4 56784bk5 [0, -1, 0, -91992, 30144048] [2] 589824
56784.bh1 56784bk6 [0, -1, 0, -2119992, 1188797232] [2] 589824

## Rank

sage: E.rank()

The elliptic curves in class 56784bk have rank $$0$$.

## Modular form 56784.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.