# Properties

 Label 106470a Number of curves $4$ Conductor $106470$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106470.l1")

sage: E.isogeny_class()

## Elliptic curves in class 106470a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.l3 106470a1 [1, -1, 0, -7890, 238356] [2] 221184 $$\Gamma_0(N)$$-optimal
106470.l4 106470a2 [1, -1, 0, 12390, 1248300] [2] 442368
106470.l1 106470a3 [1, -1, 0, -159990, -24560704] [2] 663552
106470.l2 106470a4 [1, -1, 0, -114360, -38897650] [2] 1327104

## Rank

sage: E.rank()

The elliptic curves in class 106470a have rank $$1$$.

## Modular form 106470.2.a.l

sage: E.q_eigenform(10)

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

## 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.