# Properties

 Label 10830.n Number of curves $2$ Conductor $10830$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.n1 10830o2 $$[1, 0, 1, -10838, 426506]$$ $$2992209121/54150$$ $$2547534456150$$ $$$$ $$34560$$ $$1.1758$$
10830.n2 10830o1 $$[1, 0, 1, -8, 19298]$$ $$-1/3420$$ $$-160896913020$$ $$$$ $$17280$$ $$0.82922$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10830.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10830.n do not have complex multiplication.

## Modular form 10830.2.a.n

sage: E.q_eigenform(10)

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