# Properties

 Label 209484be Number of curves 2 Conductor 209484 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("209484.bq1")

sage: E.isogeny_class()

## Elliptic curves in class 209484be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
209484.bq2 209484be1 [0, 0, 0, 12696, -304175]  608256 $$\Gamma_0(N)$$-optimal
209484.bq1 209484be2 [0, 0, 0, -58719, -2603738]  1216512

## Rank

sage: E.rank()

The elliptic curves in class 209484be have rank $$1$$.

## Modular form 209484.2.a.bq

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{7} + q^{11} - 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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. 