# Properties

 Label 58800.n Number of curves $2$ Conductor $58800$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 58800.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.n1 58800hl2 $$[0, -1, 0, -3348, -64308]$$ $$1102736/147$$ $$553420896000$$ $$$$ $$73728$$ $$0.98097$$
58800.n2 58800hl1 $$[0, -1, 0, 327, -5508]$$ $$16384/63$$ $$-14823774000$$ $$$$ $$36864$$ $$0.63440$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58800.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 58800.n do not have complex multiplication.

## Modular form 58800.2.a.n

sage: E.q_eigenform(10)

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