# Properties

 Label 189.c Number of curves $3$ Conductor $189$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 189.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189.c1 189c3 $$[0, 0, 1, -426, 3384]$$ $$35184082944/7$$ $$1701$$ $$$$ $$36$$ $$0.0093281$$
189.c2 189c2 $$[0, 0, 1, -216, -1222]$$ $$56623104/7$$ $$137781$$ $$[]$$ $$36$$ $$0.0093281$$
189.c3 189c1 $$[0, 0, 1, -6, 3]$$ $$884736/343$$ $$9261$$ $$$$ $$12$$ $$-0.53998$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 189.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 189.c do not have complex multiplication.

## Modular form189.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} + q^{7} + 6q^{11} - 4q^{13} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 