# Properties

 Label 17424.bi Number of curves 4 Conductor 17424 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17424.bi1")

sage: E.isogeny_class()

## Elliptic curves in class 17424.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.bi1 17424bm3 [0, 0, 0, -1402995, 637184306]  276480
17424.bi2 17424bm4 [0, 0, 0, -706035, 1270442162]  552960
17424.bi3 17424bm1 [0, 0, 0, -96195, -10831678]  92160 $$\Gamma_0(N)$$-optimal
17424.bi4 17424bm2 [0, 0, 0, 78045, -45714526]  184320

## Rank

sage: E.rank()

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

## Modular form 17424.2.a.bi

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 