# Properties

 Label 236992m Number of curves $2$ Conductor $236992$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 236992m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.m2 236992m1 $$[0, 1, 0, 1167327, -2283106241]$$ $$4533086375/60669952$$ $$-2354401844896026591232$$ $$$$ $$11354112$$ $$2.7816$$ $$\Gamma_0(N)$$-optimal
236992.m1 236992m2 $$[0, 1, 0, -20500513, -33454460865]$$ $$24553362849625/1755162752$$ $$68112109622265519276032$$ $$$$ $$22708224$$ $$3.1282$$

## Rank

sage: E.rank()

The elliptic curves in class 236992m have rank $$2$$.

## Complex multiplication

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

## Modular form 236992.2.a.m

sage: E.q_eigenform(10)

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