# Properties

 Label 182070ch Number of curves $4$ Conductor $182070$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("182070.cg1")

sage: E.isogeny_class()

## Elliptic curves in class 182070ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.cg3 182070ch1 [1, -1, 1, -13493, 531981]  497664 $$\Gamma_0(N)$$-optimal
182070.cg4 182070ch2 [1, -1, 1, 21187, 2793117]  995328
182070.cg1 182070ch3 [1, -1, 1, -273593, -54944459]  1492992
182070.cg2 182070ch4 [1, -1, 1, -195563, -86999183]  2985984

## Rank

sage: E.rank()

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

## Modular form 182070.2.a.cg

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 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. 