# Properties

 Label 244758.y Number of curves $2$ Conductor $244758$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 244758.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244758.y1 244758y1 $$[1, 0, 0, -178652951, 542168715753]$$ $$13403946614821979039929/5057590268826067968$$ $$237938789933949203320439808$$ $$$$ $$227635200$$ $$3.7607$$ $$\Gamma_0(N)$$-optimal
244758.y2 244758y2 $$[1, 0, 0, 558884489, 3869200107593]$$ $$410363075617640914325831/374944243169850027552$$ $$-17639582245803827184058113312$$ $$$$ $$455270400$$ $$4.1073$$

## Rank

sage: E.rank()

The elliptic curves in class 244758.y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 244758.y do not have complex multiplication.

## Modular form 244758.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 4q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + 4q^{10} + q^{12} - 4q^{14} + 4q^{15} + q^{16} - 6q^{17} + q^{18} + O(q^{20})$$ ## 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. 