# Properties

 Label 95550.co Number of curves $2$ Conductor $95550$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 95550.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.co1 95550x2 $$[1, 1, 0, -56375, 4591875]$$ $$10779215329/1232010$$ $$2264761632656250$$ $$$$ $$829440$$ $$1.6786$$
95550.co2 95550x1 $$[1, 1, 0, 4875, 365625]$$ $$6967871/35100$$ $$-64523123437500$$ $$$$ $$414720$$ $$1.3321$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 95550.co have rank $$0$$.

## Complex multiplication

The elliptic curves in class 95550.co do not have complex multiplication.

## Modular form 95550.2.a.co

sage: E.q_eigenform(10)

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