# Properties

 Label 98a Number of curves 6 Conductor 98 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("98.a1")

sage: E.isogeny_class()

## Elliptic curves in class 98a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98.a5 98a1 [1, 1, 0, -25, -111] [2] 16 $$\Gamma_0(N)$$-optimal
98.a4 98a2 [1, 1, 0, -515, -4717] [2] 32
98.a6 98a3 [1, 1, 0, 220, 2192] [2] 48
98.a3 98a4 [1, 1, 0, -1740, 22184] [2] 96
98.a2 98a5 [1, 1, 0, -8355, 291341] [2] 144
98.a1 98a6 [1, 1, 0, -133795, 18781197] [2] 288

## Rank

sage: E.rank()

The elliptic curves in class 98a have rank $$0$$.

## Modular form98.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - q^{8} + q^{9} + 2q^{12} + 4q^{13} + q^{16} - 6q^{17} - q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.