# Properties

 Label 4830k Number of curves $2$ Conductor $4830$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 4830k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.k1 4830k1 $$[1, 0, 1, -24, 22]$$ $$1439069689/579600$$ $$579600$$ $$$$ $$768$$ $$-0.19620$$ $$\Gamma_0(N)$$-optimal
4830.k2 4830k2 $$[1, 0, 1, 76, 182]$$ $$49471280711/41992020$$ $$-41992020$$ $$$$ $$1536$$ $$0.15038$$

## Rank

sage: E.rank()

The elliptic curves in class 4830k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4830k do not have complex multiplication.

## Modular form4830.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + 4q^{13} - q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 