# Properties

 Label 297024.dw Number of curves $2$ Conductor $297024$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dw1")

sage: E.isogeny_class()

## Elliptic curves in class 297024.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.dw1 297024dw1 $$[0, -1, 0, -29121, 1921473]$$ $$10418796526321/6390657$$ $$1675272388608$$ $$[2]$$ $$1146880$$ $$1.2884$$ $$\Gamma_0(N)$$-optimal
297024.dw2 297024dw2 $$[0, -1, 0, -23681, 2655873]$$ $$-5602762882081/8312741073$$ $$-2179135195840512$$ $$[2]$$ $$2293760$$ $$1.6349$$

## Rank

sage: E.rank()

The elliptic curves in class 297024.dw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 297024.dw do not have complex multiplication.

## Modular form 297024.2.a.dw

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{5} + q^{7} + q^{9} + 4q^{11} - q^{13} - 4q^{15} + q^{17} + O(q^{20})$$

## 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 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.