# Properties

 Label 141570.ed Number of curves $2$ Conductor $141570$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ed1")

sage: E.isogeny_class()

## Elliptic curves in class 141570.ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.ed1 141570h2 $$[1, -1, 1, -50117, -3855981]$$ $$10779215329/1232010$$ $$1591101452487690$$ $$[2]$$ $$983040$$ $$1.6492$$
141570.ed2 141570h1 $$[1, -1, 1, 4333, -305841]$$ $$6967871/35100$$ $$-45330525711900$$ $$[2]$$ $$491520$$ $$1.3026$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 141570.ed have rank $$0$$.

## Complex multiplication

The elliptic curves in class 141570.ed do not have complex multiplication.

## Modular form 141570.2.a.ed

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - 2q^{7} + q^{8} + q^{10} + q^{13} - 2q^{14} + q^{16} + 8q^{17} + 6q^{19} + O(q^{20})$$

## 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 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.