# Properties

 Label 5850.g Number of curves $4$ Conductor $5850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 5850.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.g1 5850j4 $$[1, -1, 0, -196329942, 1058876009716]$$ $$73474353581350183614361/576510977802240$$ $$6566820356528640000000$$ $$$$ $$829440$$ $$3.3594$$
5850.g2 5850j3 $$[1, -1, 0, -12009942, 17283689716]$$ $$-16818951115904497561/1592332281446400$$ $$-18137659893350400000000$$ $$$$ $$414720$$ $$3.0128$$
5850.g3 5850j2 $$[1, -1, 0, -3600567, -98094659]$$ $$453198971846635561/261896250564000$$ $$2983161979080562500000$$ $$$$ $$276480$$ $$2.8101$$
5850.g4 5850j1 $$[1, -1, 0, 899433, -12594659]$$ $$7064514799444439/4094064000000$$ $$-46633947750000000000$$ $$$$ $$138240$$ $$2.4635$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5850.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5850.g do not have complex multiplication.

## Modular form5850.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{7} - q^{8} - q^{13} + 2q^{14} + q^{16} + 2q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 