# Properties

 Label 17640.bq Number of curves 4 Conductor 17640 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17640.bq1")

sage: E.isogeny_class()

## Elliptic curves in class 17640.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17640.bq1 17640cs3 [0, 0, 0, -47187, -3945186]  36864
17640.bq2 17640cs2 [0, 0, 0, -3087, -55566] [2, 2] 18432
17640.bq3 17640cs1 [0, 0, 0, -882, 9261]  9216 $$\Gamma_0(N)$$-optimal
17640.bq4 17640cs4 [0, 0, 0, 5733, -314874]  36864

## Rank

sage: E.rank()

The elliptic curves in class 17640.bq have rank $$1$$.

## Modular form 17640.2.a.bq

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 