# Properties

 Label 116886.s Number of curves $2$ Conductor $116886$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 116886.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.s1 116886k2 $$[1, 0, 1, -7510231, -7922501380]$$ $$26444015547214434625/46191222$$ $$81830567437542$$ $$$$ $$2580480$$ $$2.3575$$
116886.s2 116886k1 $$[1, 0, 1, -469241, -123900856]$$ $$-6449916994998625/8532911772$$ $$-15116573711716092$$ $$$$ $$1290240$$ $$2.0110$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 116886.s have rank $$1$$.

## Complex multiplication

The elliptic curves in class 116886.s do not have complex multiplication.

## Modular form 116886.2.a.s

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + q^{12} - 6q^{13} + q^{14} + q^{16} - 4q^{17} - q^{18} + 2q^{19} + O(q^{20})$$ ## 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. 