# Properties

 Label 9800.x Number of curves $4$ Conductor $9800$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 9800.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9800.x1 9800ba3 $$[0, 0, 0, -131075, 18264750]$$ $$132304644/5$$ $$9411920000000$$ $$$$ $$27648$$ $$1.5755$$
9800.x2 9800ba2 $$[0, 0, 0, -8575, 257250]$$ $$148176/25$$ $$11764900000000$$ $$[2, 2]$$ $$13824$$ $$1.2289$$
9800.x3 9800ba1 $$[0, 0, 0, -2450, -42875]$$ $$55296/5$$ $$147061250000$$ $$$$ $$6912$$ $$0.88231$$ $$\Gamma_0(N)$$-optimal
9800.x4 9800ba4 $$[0, 0, 0, 15925, 1457750]$$ $$237276/625$$ $$-1176490000000000$$ $$$$ $$27648$$ $$1.5755$$

## Rank

sage: E.rank()

The elliptic curves in class 9800.x have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9800.x do not have complex multiplication.

## Modular form9800.2.a.x

sage: E.q_eigenform(10)

$$q - 3q^{9} + 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 