# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("10830.j1")

sage: E.isogeny_class()

## Elliptic curves in class 10830.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.j1 10830i1 [1, 0, 1, -13004, 656102]  49248 $$\Gamma_0(N)$$-optimal
10830.j2 10830i2 [1, 0, 1, 89881, -3212374] [] 147744

## Rank

sage: E.rank()

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

## 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. 