# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 1050l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.l2 1050l1 $$[1, 1, 1, 612, -219]$$ $$2595575/1512$$ $$-14765625000$$ $$[]$$ $$1080$$ $$0.64073$$ $$\Gamma_0(N)$$-optimal
1050.l1 1050l2 $$[1, 1, 1, -8763, -337719]$$ $$-7620530425/526848$$ $$-5145000000000$$ $$[]$$ $$3240$$ $$1.1900$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1050.2.a.l

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. 