# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.m1 1050m1 $$[1, 1, 1, -4263, 104781]$$ $$4386781853/27216$$ $$53156250000$$ $$$$ $$1600$$ $$0.89607$$ $$\Gamma_0(N)$$-optimal
1050.m2 1050m2 $$[1, 1, 1, -1763, 229781]$$ $$-310288733/11573604$$ $$-22604695312500$$ $$$$ $$3200$$ $$1.2426$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1050.2.a.m

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. 