# Properties

 Label 106470ew Number of curves $4$ Conductor $106470$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106470.eq1")

sage: E.isogeny_class()

## Elliptic curves in class 106470ew

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.eq4 106470ew1 [1, -1, 1, 3517, 127027] [2] 245760 $$\Gamma_0(N)$$-optimal
106470.eq3 106470ew2 [1, -1, 1, -26903, 1380331] [2, 2] 491520
106470.eq2 106470ew3 [1, -1, 1, -133373, -17486153] [2] 983040
106470.eq1 106470ew4 [1, -1, 1, -407153, 100093231] [2] 983040

## Rank

sage: E.rank()

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

## Modular form 106470.2.a.eq

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.