# Properties

 Label 9800.u Number of curves $4$ Conductor $9800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 9800.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9800.u1 9800d3 [0, 0, 0, -366275, -85321250]  49152
9800.u2 9800d4 [0, 0, 0, -72275, 5916750]  49152
9800.u3 9800d2 [0, 0, 0, -23275, -1286250] [2, 2] 24576
9800.u4 9800d1 [0, 0, 0, 1225, -85750]  12288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9800.u have rank $$0$$.

## Complex multiplication

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

## Modular form9800.2.a.u

sage: E.q_eigenform(10)

$$q - 3q^{9} - 4q^{11} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 