# Properties

 Label 58800iz Number of curves $6$ Conductor $58800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.fr1")

sage: E.isogeny_class()

## Elliptic curves in class 58800iz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.fr6 58800iz1 [0, 1, 0, 195592, -46528812] [2] 884736 $$\Gamma_0(N)$$-optimal
58800.fr5 58800iz2 [0, 1, 0, -1372408, -482432812] [2, 2] 1769472
58800.fr4 58800iz3 [0, 1, 0, -7252408, 7102767188] [2] 3538944
58800.fr2 58800iz4 [0, 1, 0, -20580408, -35940400812] [2, 2] 3538944
58800.fr3 58800iz5 [0, 1, 0, -19208408, -40937224812] [2] 7077888
58800.fr1 58800iz6 [0, 1, 0, -329280408, -2299946200812] [2] 7077888

## Rank

sage: E.rank()

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

## Modular form 58800.2.a.fr

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.