# Properties

 Label 141570bq Number of curves $6$ Conductor $141570$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141570.de1")

sage: E.isogeny_class()

## Elliptic curves in class 141570bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141570.de6 141570bq1 [1, -1, 1, 16312, 317067] [2] 655360 $$\Gamma_0(N)$$-optimal
141570.de5 141570bq2 [1, -1, 1, -70808, 2686731] [2, 2] 1310720
141570.de2 141570bq3 [1, -1, 1, -920228, 339736587] [2] 2621440
141570.de3 141570bq4 [1, -1, 1, -615308, -183750069] [2, 2] 2621440
141570.de4 141570bq5 [1, -1, 1, -125258, -468763149] [2] 5242880
141570.de1 141570bq6 [1, -1, 1, -9817358, -11837226189] [2] 5242880

## Rank

sage: E.rank()

The elliptic curves in class 141570bq have rank $$2$$.

## Modular form 141570.2.a.de

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.