# Properties

 Label 206310u Number of curves $2$ Conductor $206310$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 206310u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.bs2 206310u1 $$[1, 1, 1, 2105, 104057]$$ $$6967871/35100$$ $$-5196059703900$$ $$$$ $$570240$$ $$1.1221$$ $$\Gamma_0(N)$$-optimal
206310.bs1 206310u2 $$[1, 1, 1, -24345, 1299597]$$ $$10779215329/1232010$$ $$182381695606890$$ $$$$ $$1140480$$ $$1.4687$$

## Rank

sage: E.rank()

The elliptic curves in class 206310u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 206310u do not have complex multiplication.

## Modular form 206310.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} - q^{13} - 2q^{14} - q^{15} + q^{16} - 8q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 