# Properties

 Label 182070.be Number of curves $4$ Conductor $182070$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("182070.be1")

sage: E.isogeny_class()

## Elliptic curves in class 182070.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.be1 182070du3 [1, -1, 0, -121434, -14242060] [2] 1492992
182070.be2 182070du1 [1, -1, 0, -30399, 2045113] [2] 497664 $$\Gamma_0(N)$$-optimal
182070.be3 182070du2 [1, -1, 0, -21729, 3229435] [2] 995328
182070.be4 182070du4 [1, -1, 0, 190686, -75604852] [2] 2985984

## Rank

sage: E.rank()

The elliptic curves in class 182070.be have rank $$0$$.

## Modular form 182070.2.a.be

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 2q^{13} + q^{14} + q^{16} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.