# Properties

 Label 188760.cb Number of curves $4$ Conductor $188760$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 188760.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cb1 188760u3 $$[0, 1, 0, -200416, 34336784]$$ $$490757540836/2142075$$ $$3885892125772800$$ $$$$ $$1966080$$ $$1.8443$$
188760.cb2 188760u2 $$[0, 1, 0, -18916, -75616]$$ $$1650587344/950625$$ $$431127084960000$$ $$[2, 2]$$ $$983040$$ $$1.4977$$
188760.cb3 188760u1 $$[0, 1, 0, -13471, -604870]$$ $$9538484224/26325$$ $$746181493200$$ $$$$ $$491520$$ $$1.1511$$ $$\Gamma_0(N)$$-optimal
188760.cb4 188760u4 $$[0, 1, 0, 75464, -528640]$$ $$26198797244/15234375$$ $$-27636351600000000$$ $$$$ $$1966080$$ $$1.8443$$

## Rank

sage: E.rank()

The elliptic curves in class 188760.cb have rank $$0$$.

## Complex multiplication

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

## Modular form 188760.2.a.cb

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 LMFDB 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 LMFDB labels. 