# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 10830c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.b2 10830c1 $$[1, 1, 0, 192767, 96438973]$$ $$129205871/729000$$ $$-4469547301936929000$$ $$[]$$ $$246240$$ $$2.2607$$ $$\Gamma_0(N)$$-optimal
10830.b1 10830c2 $$[1, 1, 0, -11536123, 15092997727]$$ $$-27692833539889/35156250$$ $$-215545298125816406250$$ $$[]$$ $$738720$$ $$2.8100$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10830.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 3q^{11} - q^{12} - 2q^{13} + q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 