# Properties

 Label 10830j Number of curves $2$ Conductor $10830$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 10830j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.l2 10830j1 $$[1, 0, 1, -81594, 9229852]$$ $$-186169411/6480$$ $$-2091016281607920$$ $$[2]$$ $$72960$$ $$1.7126$$ $$\Gamma_0(N)$$-optimal
10830.l1 10830j2 $$[1, 0, 1, -1316214, 581105836]$$ $$781484460931/900$$ $$290418928001100$$ $$[2]$$ $$145920$$ $$2.0592$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.j

sage: E.q_eigenform(10)

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

## 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 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.