# Properties

 Label 10830p Number of curves 4 Conductor 10830 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10830.p1")

sage: E.isogeny_class()

## Elliptic curves in class 10830p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.p4 10830p1 [1, 0, 1, -685908, -228577454]  345600 $$\Gamma_0(N)$$-optimal
10830.p3 10830p2 [1, 0, 1, -11111588, -14257372462] [2, 2] 691200
10830.p1 10830p3 [1, 0, 1, -177785288, -912428607022]  1382400
10830.p2 10830p4 [1, 0, 1, -11248768, -13887315694]  1382400

## Rank

sage: E.rank()

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

## Modular form 10830.2.a.p

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 