# Properties

 Label 352800.cz Number of curves $4$ Conductor $352800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cz1")

sage: E.isogeny_class()

## Elliptic curves in class 352800.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.cz1 352800cz2 $$[0, 0, 0, -12351675, 16708473250]$$ $$303735479048/105$$ $$72043541640000000$$ $$$$ $$14155776$$ $$2.5906$$
352800.cz2 352800cz4 $$[0, 0, 0, -1602300, -389648000]$$ $$82881856/36015$$ $$197687478260160000000$$ $$$$ $$14155776$$ $$2.5906$$
352800.cz3 352800cz1 $$[0, 0, 0, -775425, 258622000]$$ $$601211584/11025$$ $$945571484025000000$$ $$[2, 2]$$ $$7077888$$ $$2.2440$$ $$\Gamma_0(N)$$-optimal
352800.cz4 352800cz3 $$[0, 0, 0, -3675, 750226750]$$ $$-8/354375$$ $$-243146953035000000000$$ $$$$ $$14155776$$ $$2.5906$$

## Rank

sage: E.rank()

The elliptic curves in class 352800.cz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 352800.cz do not have complex multiplication.

## Modular form 352800.2.a.cz

sage: E.q_eigenform(10)

$$q - 4q^{11} + 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 