# Properties

 Label 76050.co Number of curves $2$ Conductor $76050$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

## Elliptic curves in class 76050.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.co1 76050bl2 $$[1, -1, 0, -1749942, 798626466]$$ $$10779215329/1232010$$ $$67736367202962656250$$ $$$$ $$3096576$$ $$2.5375$$
76050.co2 76050bl1 $$[1, -1, 0, 151308, 62842716]$$ $$6967871/35100$$ $$-1929811031423437500$$ $$$$ $$1548288$$ $$2.1909$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 76050.co have rank $$0$$.

## Complex multiplication

The elliptic curves in class 76050.co do not have complex multiplication.

## Modular form 76050.2.a.co

sage: E.q_eigenform(10)

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