# Properties

 Label 236992.cm Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cm1 236992cm2 $$[0, -1, 0, -17633, 517793]$$ $$125000/49$$ $$237691160526848$$ $$[2]$$ $$720896$$ $$1.4571$$
236992.cm2 236992cm1 $$[0, -1, 0, 3527, 56505]$$ $$8000/7$$ $$-4244485009408$$ $$[2]$$ $$360448$$ $$1.1105$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.cm

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} - 4q^{11} + 4q^{13} + 2q^{17} - 6q^{19} + O(q^{20})$$

## 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.