# Properties

 Label 236992.i Number of curves $2$ Conductor $236992$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.i1 236992i2 $$[0, 1, 0, -5891649, 5495580607]$$ $$582810602977/829472$$ $$32189087723187863552$$ $$$$ $$8110080$$ $$2.6461$$
236992.i2 236992i1 $$[0, 1, 0, -474689, 32034751]$$ $$304821217/164864$$ $$6397831100260941824$$ $$$$ $$4055040$$ $$2.2995$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.i have rank $$1$$.

## Complex multiplication

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

## Modular form 236992.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{11} + 4q^{13} + 4q^{15} + 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 