# Properties

 Label 9702ca Number of curves $4$ Conductor $9702$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 9702ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bu3 9702ca1 $$[1, -1, 1, -2435, 44223]$$ $$18609625/1188$$ $$101890151748$$ $$[2]$$ $$11520$$ $$0.86288$$ $$\Gamma_0(N)$$-optimal
9702.bu4 9702ca2 $$[1, -1, 1, 1975, 183579]$$ $$9938375/176418$$ $$-15130687534578$$ $$[2]$$ $$23040$$ $$1.2095$$
9702.bu1 9702ca3 $$[1, -1, 1, -35510, -2556795]$$ $$57736239625/255552$$ $$21917703753792$$ $$[2]$$ $$34560$$ $$1.4122$$
9702.bu2 9702ca4 $$[1, -1, 1, -17870, -5111067]$$ $$-7357983625/127552392$$ $$-10939673886111432$$ $$[2]$$ $$69120$$ $$1.7588$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9702.2.a.ca

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.