# Properties

 Label 1050.d Number of curves $2$ Conductor $1050$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.d1 1050e1 $$[1, 1, 0, -80, 0]$$ $$461889917/263424$$ $$32928000$$ $$$$ $$384$$ $$0.13228$$ $$\Gamma_0(N)$$-optimal
1050.d2 1050e2 $$[1, 1, 0, 320, 400]$$ $$28849701763/16941456$$ $$-2117682000$$ $$$$ $$768$$ $$0.47886$$

## Rank

sage: E.rank()

The elliptic curves in class 1050.d have rank $$1$$.

## Complex multiplication

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

## Modular form1050.2.a.d

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. 