# Properties

 Label 9702.q Number of curves $2$ Conductor $9702$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("q1")

E.isogeny_class()

## Elliptic curves in class 9702.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.q1 9702q2 $$[1, -1, 0, -472131, -124745643]$$ $$46546832455691959/748268928$$ $$187102400639616$$ $$[2]$$ $$86016$$ $$1.8714$$
9702.q2 9702q1 $$[1, -1, 0, -28611, -2068011]$$ $$-10358806345399/1445216256$$ $$-361371989164032$$ $$[2]$$ $$43008$$ $$1.5249$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9702.q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9702.q do not have complex multiplication.

## Modular form9702.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2 q^{5} - q^{8} - 2 q^{10} - q^{11} - 4 q^{13} + q^{16} + 6 q^{17} - 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.