# Properties

 Label 9702.bz Number of curves $2$ Conductor $9702$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 9702.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bz1 9702bw2 $$[1, -1, 1, -103424, -12776137]$$ $$1426487591593/2156$$ $$184911756876$$ $$$$ $$36864$$ $$1.4299$$
9702.bz2 9702bw1 $$[1, -1, 1, -6404, -202345]$$ $$-338608873/13552$$ $$-1162302471792$$ $$$$ $$18432$$ $$1.0834$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9702.2.a.bz

sage: E.q_eigenform(10)

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

## 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. 