# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14784.w1")

sage: E.isogeny_class()

## Elliptic curves in class 14784.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14784.w1 14784br5 [0, -1, 0, -289217, 59962977] [2] 81920
14784.w2 14784br3 [0, -1, 0, -18177, 930465] [2, 2] 40960
14784.w3 14784br2 [0, -1, 0, -2497, -26015] [2, 2] 20480
14784.w4 14784br1 [0, -1, 0, -2177, -38367] [2] 10240 $$\Gamma_0(N)$$-optimal
14784.w5 14784br6 [0, -1, 0, 1983, 2861793] [2] 81920
14784.w6 14784br4 [0, -1, 0, 8063, -197087] [2] 40960

## Rank

sage: E.rank()

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

## Modular form 14784.2.a.w

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.