# Properties

 Label 14784bm Number of curves 6 Conductor 14784 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14784.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 14784bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14784.cj4 14784bm1 [0, 1, 0, -2177, 38367] [2] 10240 $$\Gamma_0(N)$$-optimal
14784.cj3 14784bm2 [0, 1, 0, -2497, 26015] [2, 2] 20480
14784.cj2 14784bm3 [0, 1, 0, -18177, -930465] [2, 2] 40960
14784.cj6 14784bm4 [0, 1, 0, 8063, 197087] [2] 40960
14784.cj1 14784bm5 [0, 1, 0, -289217, -59962977] [2] 81920
14784.cj5 14784bm6 [0, 1, 0, 1983, -2861793] [2] 81920

## Rank

sage: E.rank()

The elliptic curves in class 14784bm have rank $$0$$.

## Modular form 14784.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{7} + q^{9} + q^{11} - 6q^{13} + 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.