# Properties

 Label 10830.j Number of curves $2$ Conductor $10830$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 10830.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.j1 10830i1 $$[1, 0, 1, -13004, 656102]$$ $$-14317849/2700$$ $$-45855620210700$$ $$$$ $$49248$$ $$1.3455$$ $$\Gamma_0(N)$$-optimal
10830.j2 10830i2 $$[1, 0, 1, 89881, -3212374]$$ $$4728305591/3000000$$ $$-50950689123000000$$ $$[]$$ $$147744$$ $$1.8948$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.j

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 