# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.k1 58800bh2 $$[0, -1, 0, -122908, -15676688]$$ $$1272112/75$$ $$12106082100000000$$ $$$$ $$516096$$ $$1.8393$$
58800.k2 58800bh1 $$[0, -1, 0, 5717, -1013438]$$ $$2048/45$$ $$-453978078750000$$ $$$$ $$258048$$ $$1.4927$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 58800.2.a.k

sage: E.q_eigenform(10)

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