# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 1050j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.j2 1050j1 $$[1, 0, 1, 24, -2]$$ $$2595575/1512$$ $$-945000$$ $$$$ $$216$$ $$-0.16399$$ $$\Gamma_0(N)$$-optimal
1050.j1 1050j2 $$[1, 0, 1, -351, -2702]$$ $$-7620530425/526848$$ $$-329280000$$ $$[]$$ $$648$$ $$0.38532$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1050.2.a.j

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 