# Properties

 Label 4620j Number of curves $4$ Conductor $4620$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 4620j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.j3 4620j1 $$[0, 1, 0, -2661, 52740]$$ $$-130287139815424/2250652635$$ $$-36010442160$$ $$$$ $$5184$$ $$0.82354$$ $$\Gamma_0(N)$$-optimal
4620.j2 4620j2 $$[0, 1, 0, -42756, 3388644]$$ $$33766427105425744/9823275$$ $$2514758400$$ $$$$ $$10368$$ $$1.1701$$
4620.j4 4620j3 $$[0, 1, 0, 10299, 260424]$$ $$7549996227362816/6152409907875$$ $$-98438558526000$$ $$$$ $$15552$$ $$1.3728$$
4620.j1 4620j4 $$[0, 1, 0, -49596, 2224980]$$ $$52702650535889104/22020583921875$$ $$5637269484000000$$ $$$$ $$31104$$ $$1.7194$$

## Rank

sage: E.rank()

The elliptic curves in class 4620j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4620j do not have complex multiplication.

## Modular form4620.2.a.j

sage: E.q_eigenform(10)

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