# Properties

 Label 179520dx Number of curves 6 Conductor 179520 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("179520.v1")

sage: E.isogeny_class()

## Elliptic curves in class 179520dx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.v4 179520dx1 [0, -1, 0, -467841, -123011295] [2] 1179648 $$\Gamma_0(N)$$-optimal
179520.v3 179520dx2 [0, -1, 0, -472961, -120175839] [2, 2] 2359296
179520.v2 179520dx3 [0, -1, 0, -1272961, 394544161] [2, 2] 4718592
179520.v5 179520dx4 [0, -1, 0, 245119, -453508575] [2] 4718592
179520.v1 179520dx5 [0, -1, 0, -18696961, 31120025761] [4] 9437184
179520.v6 179520dx6 [0, -1, 0, 3351039, 2598342561] [2] 9437184

## Rank

sage: E.rank()

The elliptic curves in class 179520dx have rank $$1$$.

## Modular form 179520.2.a.v

sage: E.q_eigenform(10)

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

## 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.