# Properties

 Label 257600.y Number of curves $2$ Conductor $257600$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 257600.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.y1 257600y2 $$[0, 1, 0, -48833, -4169537]$$ $$12576878500/1127$$ $$1154048000000$$ $$$$ $$737280$$ $$1.3545$$
257600.y2 257600y1 $$[0, 1, 0, -2833, -75537]$$ $$-9826000/3703$$ $$-947968000000$$ $$$$ $$368640$$ $$1.0080$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 257600.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 257600.y do not have complex multiplication.

## Modular form 257600.2.a.y

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} + 4q^{11} + 6q^{13} + O(q^{20})$$ ## 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. 