# Properties

 Label 25350cw Number of curves $2$ Conductor $25350$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 25350cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.dh2 25350cw1 $$[1, 0, 0, 16812, -2327508]$$ $$6967871/35100$$ $$-2647203060937500$$ $$[2]$$ $$193536$$ $$1.6416$$ $$\Gamma_0(N)$$-optimal
25350.dh1 25350cw2 $$[1, 0, 0, -194438, -29578758]$$ $$10779215329/1232010$$ $$92916827438906250$$ $$[2]$$ $$387072$$ $$1.9881$$

## Rank

sage: E.rank()

The elliptic curves in class 25350cw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 25350cw do not have complex multiplication.

## Modular form 25350.2.a.cw

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} + 2q^{14} + q^{16} - 8q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.