# Properties

 Label 17424bw Number of curves 4 Conductor 17424 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17424.by1")
sage: E.isogeny_class()

## Elliptic curves in class 17424bw

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
17424.by3 17424bw1 [0, 0, 0, -113619, 14617042] 2 92160 $$\Gamma_0(N)$$-optimal
17424.by2 17424bw2 [0, 0, 0, -200739, -10874270] 4 184320
17424.by1 17424bw3 [0, 0, 0, -2552979, -1568527598] 2 368640
17424.by4 17424bw4 [0, 0, 0, 757581, -84664910] 2 368640

## Rank

sage: E.rank()

The elliptic curves in class 17424bw have rank $$0$$.

## Modular form 17424.2.a.by

sage: E.q_eigenform(10)
$$q + 2q^{5} + 4q^{7} + 2q^{13} - 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.