# Properties

 Label 10830.p Number of curves $4$ Conductor $10830$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10830.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.p1 10830p3 $$[1, 0, 1, -177785288, -912428607022]$$ $$13209596798923694545921/92340$$ $$4344216651540$$ $$[2]$$ $$1382400$$ $$2.9597$$
10830.p2 10830p4 $$[1, 0, 1, -11248768, -13887315694]$$ $$3345930611358906241/165622259047500$$ $$7791845090099858347500$$ $$[4]$$ $$1382400$$ $$2.9597$$
10830.p3 10830p2 $$[1, 0, 1, -11111588, -14257372462]$$ $$3225005357698077121/8526675600$$ $$401144965603203600$$ $$[2, 2]$$ $$691200$$ $$2.6131$$
10830.p4 10830p1 $$[1, 0, 1, -685908, -228577454]$$ $$-758575480593601/40535043840$$ $$-1907006848826423040$$ $$[2]$$ $$345600$$ $$2.2666$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.