# Properties

 Label 5850.x Number of curves $2$ Conductor $5850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 5850.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.x1 5850z2 $$[1, -1, 0, -81882, 8330476]$$ $$666276475992821/58199166792$$ $$5303399073921000$$ $$$$ $$49152$$ $$1.7578$$
5850.x2 5850z1 $$[1, -1, 0, -80082, 8742676]$$ $$623295446073461/5458752$$ $$497428776000$$ $$$$ $$24576$$ $$1.4112$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5850.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4 q^{7} - q^{8} - 2 q^{11} + q^{13} - 4 q^{14} + q^{16} - 4 q^{17} + 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 