# Properties

 Label 1050.r Number of curves $2$ Conductor $1050$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.r1 1050o2 $$[1, 0, 0, -109388, -13934358]$$ $$-14822892630025/42$$ $$-410156250$$ $$[]$$ $$3000$$ $$1.3093$$
1050.r2 1050o1 $$[1, 0, 0, 22, -2748]$$ $$46969655/130691232$$ $$-3267280800$$ $$$$ $$600$$ $$0.50455$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1050.r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1050.r do not have complex multiplication.

## Modular form1050.2.a.r

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} - q^{13} + q^{14} + q^{16} + 3q^{17} + q^{18} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 