# Properties

 Label 187200cc Number of curves $2$ Conductor $187200$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 187200cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pt2 187200cc1 $$[0, 0, 0, -178500, -29000000]$$ $$107850176/117$$ $$682344000000000$$ $$$$ $$1146880$$ $$1.7620$$ $$\Gamma_0(N)$$-optimal
187200.pt1 187200cc2 $$[0, 0, 0, -223500, -13250000]$$ $$26463592/13689$$ $$638673984000000000$$ $$$$ $$2293760$$ $$2.1085$$

## Rank

sage: E.rank()

The elliptic curves in class 187200cc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 187200cc do not have complex multiplication.

## Modular form 187200.2.a.cc

sage: E.q_eigenform(10)

$$q + 4q^{7} + 2q^{11} - q^{13} + 2q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 