Properties

 Label 169650eo Number of curves $4$ Conductor $169650$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("eo1")

sage: E.isogeny_class()

Elliptic curves in class 169650eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169650.cx3 169650eo1 $$[1, -1, 0, -398817, -96838659]$$ $$615882348586441/21715200$$ $$247349700000000$$ $$$$ $$2359296$$ $$1.8516$$ $$\Gamma_0(N)$$-optimal
169650.cx2 169650eo2 $$[1, -1, 0, -416817, -87604659]$$ $$703093388853961/115124490000$$ $$1311339893906250000$$ $$[2, 2]$$ $$4718592$$ $$2.1982$$
169650.cx1 169650eo3 $$[1, -1, 0, -1879317, 908357841]$$ $$64443098670429961/6032611833300$$ $$68715219163682812500$$ $$$$ $$9437184$$ $$2.5448$$
169650.cx4 169650eo4 $$[1, -1, 0, 757683, -492807159]$$ $$4223169036960119/11647532812500$$ $$-132672678442382812500$$ $$$$ $$9437184$$ $$2.5448$$

Rank

sage: E.rank()

The elliptic curves in class 169650eo have rank $$0$$.

Complex multiplication

The elliptic curves in class 169650eo do not have complex multiplication.

Modular form 169650.2.a.eo

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4 q^{7} - q^{8} + 4 q^{11} - q^{13} - 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})$$ 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 