# Properties

 Label 4830l Number of curves $4$ Conductor $4830$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 4830l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.l3 4830l1 $$[1, 0, 1, -127124, 18674066]$$ $$-227196402372228188089/19338934824115200$$ $$-19338934824115200$$ $$$$ $$46080$$ $$1.8699$$ $$\Gamma_0(N)$$-optimal
4830.l2 4830l2 $$[1, 0, 1, -2073844, 1149329042]$$ $$986396822567235411402169/6336721794060000$$ $$6336721794060000$$ $$$$ $$92160$$ $$2.2165$$
4830.l4 4830l3 $$[1, 0, 1, 753661, 753662]$$ $$47342661265381757089751/27397579603968000000$$ $$-27397579603968000000$$ $$$$ $$138240$$ $$2.4192$$
4830.l1 4830l4 $$[1, 0, 1, -3014659, 5275646]$$ $$3029968325354577848895529/1753440696000000000000$$ $$1753440696000000000000$$ $$$$ $$276480$$ $$2.7658$$

## Rank

sage: E.rank()

The elliptic curves in class 4830l have rank $$0$$.

## Complex multiplication

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

## Modular form4830.2.a.l

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 