# Properties

 Label 19404r Number of curves 2 Conductor 19404 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19404.y1")

sage: E.isogeny_class()

## Elliptic curves in class 19404r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19404.y2 19404r1 [0, 0, 0, 1176, -8575]  17280 $$\Gamma_0(N)$$-optimal
19404.y1 19404r2 [0, 0, 0, -5439, -73402]  34560

## Rank

sage: E.rank()

The elliptic curves in class 19404r have rank $$0$$.

## Modular form 19404.2.a.y

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{11} + 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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. 