# Properties

 Label 19600ck Number of curves 2 Conductor 19600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 19600ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bf2 19600ck1 [0, -1, 0, 3512, 66032] [] 27648 $$\Gamma_0(N)$$-optimal
19600.bf1 19600ck2 [0, -1, 0, -35688, -3634448] [] 82944

## Rank

sage: E.rank()

The elliptic curves in class 19600ck have rank $$1$$.

## Modular form 19600.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{9} - 3q^{11} + 2q^{13} + 3q^{17} - 7q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.