# Properties

 Label 172480du Number of curves 4 Conductor 172480 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("172480.gf1")

sage: E.isogeny_class()

## Elliptic curves in class 172480du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
172480.gf3 172480du1 [0, -1, 0, -175681, 551610081] [2] 5308416 $$\Gamma_0(N)$$-optimal
172480.gf2 172480du2 [0, -1, 0, -11214401, 14330140385] [2] 10616832
172480.gf4 172480du3 [0, -1, 0, 1580479, -14857991455] [2] 15925248
172480.gf1 172480du4 [0, -1, 0, -81899841, -277169852959] [2] 31850496

## Rank

sage: E.rank()

The elliptic curves in class 172480du have rank $$1$$.

## Modular form 172480.2.a.gf

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.