# Properties

 Label 19600cw Number of curves 2 Conductor 19600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 19600cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.ba2 19600cw1 [0, 1, 0, -28408, -2176812]  92160 $$\Gamma_0(N)$$-optimal
19600.ba1 19600cw2 [0, 1, 0, -476408, -126720812]  184320

## Rank

sage: E.rank()

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

## Modular form 19600.2.a.ba

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{9} + 4q^{11} + 2q^{13} + 8q^{17} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 