# Properties

 Label 60333.n Number of curves $2$ Conductor $60333$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 60333.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60333.n1 60333l1 $$[1, 0, 1, -76899, 8197009]$$ $$10418796526321/6390657$$ $$30846480723513$$ $$$$ $$376320$$ $$1.5311$$ $$\Gamma_0(N)$$-optimal
60333.n2 60333l2 $$[1, 0, 1, -62534, 11357309]$$ $$-5602762882081/8312741073$$ $$-40124013425826057$$ $$$$ $$752640$$ $$1.8777$$

## Rank

sage: E.rank()

The elliptic curves in class 60333.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 60333.n do not have complex multiplication.

## Modular form 60333.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} + 4q^{10} + 4q^{11} - q^{12} - q^{14} + 4q^{15} - q^{16} + q^{17} + q^{18} + O(q^{20})$$ ## 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. 