# Properties

 Label 2850.x Number of curves $2$ Conductor $2850$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 2850.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.x1 2850ba1 $$[1, 0, 0, -2388, -45108]$$ $$96386901625/18468$$ $$288562500$$ $$[2]$$ $$2880$$ $$0.62403$$ $$\Gamma_0(N)$$-optimal
2850.x2 2850ba2 $$[1, 0, 0, -2138, -54858]$$ $$-69173457625/42633378$$ $$-666146531250$$ $$[2]$$ $$5760$$ $$0.97060$$

## Rank

sage: E.rank()

The elliptic curves in class 2850.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2850.x do not have complex multiplication.

## Modular form2850.2.a.x

sage: E.q_eigenform(10)

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

## 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.