# Properties

 Label 17424.l Number of curves 2 Conductor 17424 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17424.l1")

sage: E.isogeny_class()

## Elliptic curves in class 17424.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.l1 17424by2 [0, 0, 0, -13431, 284834] [2] 46080
17424.l2 17424by1 [0, 0, 0, 2904, 33275] [2] 23040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 17424.2.a.l

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.