# Properties

 Label 240669p Number of curves $6$ Conductor $240669$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("240669.p1")

sage: E.isogeny_class()

## Elliptic curves in class 240669p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
240669.p4 240669p1 [1, -1, 1, -586994, 173247000] [2] 1310720 $$\Gamma_0(N)$$-optimal
240669.p3 240669p2 [1, -1, 1, -592439, 169873278] [2, 2] 2621440
240669.p5 240669p3 [1, -1, 1, 240646, 609075690] [2] 5242880
240669.p2 240669p4 [1, -1, 1, -1512644, -485312682] [2, 2] 5242880
240669.p6 240669p5 [1, -1, 1, 4220941, -3290182464] [2] 10485760
240669.p1 240669p6 [1, -1, 1, -21969509, -39623386800] [2] 10485760

## Rank

sage: E.rank()

The elliptic curves in class 240669p have rank $$0$$.

## Modular form 240669.2.a.p

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 2q^{10} - q^{13} - q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.