# Properties

 Label 10830v Number of curves $8$ Conductor $10830$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 10830v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.q8 10830v1 $$[1, 1, 1, 534, -14361]$$ $$357911/2160$$ $$-101619102960$$ $$[2]$$ $$13824$$ $$0.79393$$ $$\Gamma_0(N)$$-optimal
10830.q6 10830v2 $$[1, 1, 1, -6686, -193417]$$ $$702595369/72900$$ $$3429644724900$$ $$[2, 2]$$ $$27648$$ $$1.1405$$
10830.q7 10830v3 $$[1, 1, 1, -4881, 427503]$$ $$-273359449/1536000$$ $$-72262473216000$$ $$[2]$$ $$41472$$ $$1.3432$$
10830.q4 10830v4 $$[1, 1, 1, -104156, -12981481]$$ $$2656166199049/33750$$ $$1587798483750$$ $$[2]$$ $$55296$$ $$1.4871$$
10830.q5 10830v5 $$[1, 1, 1, -24736, 1279463]$$ $$35578826569/5314410$$ $$250021100445210$$ $$[2]$$ $$55296$$ $$1.4871$$
10830.q3 10830v6 $$[1, 1, 1, -120401, 15999599]$$ $$4102915888729/9000000$$ $$423412929000000$$ $$[2, 2]$$ $$82944$$ $$1.6898$$
10830.q2 10830v7 $$[1, 1, 1, -163721, 3402143]$$ $$10316097499609/5859375000$$ $$275659458984375000$$ $$[2]$$ $$165888$$ $$2.0364$$
10830.q1 10830v8 $$[1, 1, 1, -1925401, 1027521599]$$ $$16778985534208729/81000$$ $$3810716361000$$ $$[2]$$ $$165888$$ $$2.0364$$

## Rank

sage: E.rank()

The elliptic curves in class 10830v have rank $$1$$.

## Complex multiplication

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

## Modular form 10830.2.a.v

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.