# Properties

 Label 17424bu Number of curves $2$ Conductor $17424$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 17424bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.s2 17424bu1 [0, 0, 0, -4323, -109406] [] 9216 $$\Gamma_0(N)$$-optimal
17424.s1 17424bu2 [0, 0, 0, -43923, 13850386] [] 101376

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 17424bu do not have complex multiplication.

## Modular form 17424.2.a.bu

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.