# Properties

 Label 17600.w Number of curves 4 Conductor 17600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17600.w1")

sage: E.isogeny_class()

## Elliptic curves in class 17600.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17600.w1 17600r4 [0, 1, 0, -710033, -230521937]  165888
17600.w2 17600r3 [0, 1, 0, -44533, -3586437]  82944
17600.w3 17600r2 [0, 1, 0, -10033, -221937]  55296
17600.w4 17600r1 [0, 1, 0, -4533, 113563]  27648 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 17600.w have rank $$0$$.

## Modular form 17600.2.a.w

sage: E.q_eigenform(10)

$$q - 2q^{3} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 