# Properties

 Label 98736bz Number of curves 6 Conductor 98736 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("98736.n1")

sage: E.isogeny_class()

## Elliptic curves in class 98736bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98736.n5 98736bz1 [0, -1, 0, -65864, 6055920] [2] 491520 $$\Gamma_0(N)$$-optimal
98736.n4 98736bz2 [0, -1, 0, -220744, -32849936] [2, 2] 983040
98736.n6 98736bz3 [0, -1, 0, 437496, -191880720] [2] 1966080
98736.n2 98736bz4 [0, -1, 0, -3357064, -2366272016] [2, 2] 1966080
98736.n3 98736bz5 [0, -1, 0, -3182824, -2623032080] [2] 3932160
98736.n1 98736bz6 [0, -1, 0, -53712424, -151498706192] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 98736bz have rank $$1$$.

## Modular form 98736.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} + 2q^{13} + 2q^{15} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.