# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.s1 236992s2 $$[0, 1, 0, -2177, -38657]$$ $$1431644/49$$ $$39071449088$$ $$$$ $$172032$$ $$0.80427$$
236992.s2 236992s1 $$[0, 1, 0, -337, 1455]$$ $$21296/7$$ $$1395408896$$ $$$$ $$86016$$ $$0.45770$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.s

sage: E.q_eigenform(10)

$$q - 2 q^{3} + 2 q^{5} - q^{7} + q^{9} + 2 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})$$ ## 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. 