# Properties

 Label 188760cc Number of curves $4$ Conductor $188760$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 188760cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bd4 188760cc1 $$[0, -1, 0, -2460, -165900]$$ $$-3631696/24375$$ $$-11054540640000$$ $$$$ $$491520$$ $$1.1862$$ $$\Gamma_0(N)$$-optimal
188760.bd3 188760cc2 $$[0, -1, 0, -62960, -6046500]$$ $$15214885924/38025$$ $$68980333593600$$ $$[2, 2]$$ $$983040$$ $$1.5328$$
188760.bd2 188760cc3 $$[0, -1, 0, -87160, -945140]$$ $$20183398562/11567205$$ $$41967634958346240$$ $$$$ $$1966080$$ $$1.8793$$
188760.bd1 188760cc4 $$[0, -1, 0, -1006760, -388474260]$$ $$31103978031362/195$$ $$707490600960$$ $$$$ $$1966080$$ $$1.8793$$

## Rank

sage: E.rank()

The elliptic curves in class 188760cc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 188760cc do not have complex multiplication.

## Modular form 188760.2.a.cc

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 4q^{7} + q^{9} - q^{13} - q^{15} - 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 