# Properties

 Label 106470fh Number of curves $6$ Conductor $106470$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106470.fi1")

sage: E.isogeny_class()

## Elliptic curves in class 106470fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.fi6 106470fh1 [1, -1, 1, 15178, 1003461] [2] 589824 $$\Gamma_0(N)$$-optimal
106470.fi5 106470fh2 [1, -1, 1, -106502, 10445829] [2, 2] 1179648
106470.fi4 106470fh3 [1, -1, 1, -562802, -153457131] [2] 2359296
106470.fi2 106470fh4 [1, -1, 1, -1597082, 777200181] [2, 2] 2359296
106470.fi3 106470fh5 [1, -1, 1, -1490612, 885203349] [2] 4718592
106470.fi1 106470fh6 [1, -1, 1, -25552832, 49723588581] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 106470fh have rank $$0$$.

## Modular form 106470.2.a.fi

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 4q^{11} - q^{14} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.