# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 9702.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.c1 9702d2 $$[1, -1, 0, -2969556, -1968891184]$$ $$-61279455929796531/681472$$ $$-32205605515776$$ $$[]$$ $$155520$$ $$2.1610$$
9702.c2 9702d1 $$[1, -1, 0, -34701, -2994867]$$ $$-71285434106859/18863581528$$ $$-1222869399715656$$ $$$$ $$51840$$ $$1.6117$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9702.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} + q^{11} + 2 q^{13} + q^{16} + 3 q^{17} + 2 q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 