# Properties

 Label 9800ba Number of curves 4 Conductor 9800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9800.x1")

sage: E.isogeny_class()

## Elliptic curves in class 9800ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9800.x3 9800ba1 [0, 0, 0, -2450, -42875]  6912 $$\Gamma_0(N)$$-optimal
9800.x2 9800ba2 [0, 0, 0, -8575, 257250] [2, 2] 13824
9800.x1 9800ba3 [0, 0, 0, -131075, 18264750]  27648
9800.x4 9800ba4 [0, 0, 0, 15925, 1457750]  27648

## Rank

sage: E.rank()

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

## 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 Cremona 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 Cremona labels. 