# Properties

 Label 9702.u Number of curves $2$ Conductor $9702$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 9702.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.u1 9702e2 $$[1, -1, 0, -229371, 42339429]$$ $$144106117295241933/247808$$ $$2294949888$$ $$[2]$$ $$39424$$ $$1.4851$$
9702.u2 9702e1 $$[1, -1, 0, -14331, 664677]$$ $$-35148950502093/46137344$$ $$-427277942784$$ $$[2]$$ $$19712$$ $$1.1385$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9702.u have rank $$0$$.

## Complex multiplication

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

## Modular form9702.2.a.u

sage: E.q_eigenform(10)

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

## 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.