# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.g1 1050i1 $$[1, 0, 1, -171, 838]$$ $$4386781853/27216$$ $$3402000$$ $$$$ $$320$$ $$0.091347$$ $$\Gamma_0(N)$$-optimal
1050.g2 1050i2 $$[1, 0, 1, -71, 1838]$$ $$-310288733/11573604$$ $$-1446700500$$ $$$$ $$640$$ $$0.43792$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1050.2.a.g

sage: E.q_eigenform(10)

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