# Properties

 Label 236992.cb Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 236992.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cb1 236992cb2 $$[0, -1, 0, -85345, -9452799]$$ $$3543122/49$$ $$950764642107392$$ $$$$ $$1441792$$ $$1.6797$$
236992.cb2 236992cb1 $$[0, -1, 0, -705, -396319]$$ $$-4/7$$ $$-67911760150528$$ $$$$ $$720896$$ $$1.3331$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 236992.cb do not have complex multiplication.

## Modular form 236992.2.a.cb

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{5} + q^{7} + q^{9} - 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 