# Properties

 Label 17640.cq Number of curves $6$ Conductor $17640$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17640.cq1")

sage: E.isogeny_class()

## Elliptic curves in class 17640.cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17640.cq1 17640bd5 [0, 0, 0, -4621827, -3824361506] [2] 393216
17640.cq2 17640bd3 [0, 0, 0, -300027, -54887546] [2, 2] 196608
17640.cq3 17640bd2 [0, 0, 0, -79527, 7778554] [2, 2] 98304
17640.cq4 17640bd1 [0, 0, 0, -77322, 8275561] [4] 49152 $$\Gamma_0(N)$$-optimal
17640.cq5 17640bd4 [0, 0, 0, 105693, 38636206] [2] 196608
17640.cq6 17640bd6 [0, 0, 0, 493773, -296043986] [2] 393216

## Rank

sage: E.rank()

The elliptic curves in class 17640.cq have rank $$0$$.

## Modular form 17640.2.a.cq

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.