# Properties

 Label 2800.x Number of curves $2$ Conductor $2800$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2800.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.x1 2800u2 $$[0, 1, 0, -728, 10388]$$ $$-417267265/235298$$ $$-24094515200$$ $$[]$$ $$1728$$ $$0.69528$$
2800.x2 2800u1 $$[0, 1, 0, 72, -172]$$ $$397535/392$$ $$-40140800$$ $$[]$$ $$576$$ $$0.14598$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2800.x have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2800.x do not have complex multiplication.

## Modular form2800.2.a.x

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} - 2q^{9} - 3q^{11} - 2q^{13} - 3q^{17} + 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.