# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.p1 1050r1 $$[1, 0, 0, -2013, 4017]$$ $$461889917/263424$$ $$514500000000$$ $$$$ $$1920$$ $$0.93700$$ $$\Gamma_0(N)$$-optimal
1050.p2 1050r2 $$[1, 0, 0, 7987, 34017]$$ $$28849701763/16941456$$ $$-33088781250000$$ $$$$ $$3840$$ $$1.2836$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1050.2.a.p

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} + 6q^{13} - q^{14} + q^{16} + 4q^{17} + q^{18} - 6q^{19} + O(q^{20})$$ ## 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 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. 