Properties

 Label 169650dy Number of curves $2$ Conductor $169650$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("dy1")

sage: E.isogeny_class()

Elliptic curves in class 169650dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169650.bo1 169650dy1 $$[1, -1, 0, -187317, -26499659]$$ $$63812982460681/10201800960$$ $$116204889060000000$$ $$$$ $$1474560$$ $$1.9969$$ $$\Gamma_0(N)$$-optimal
169650.bo2 169650dy2 $$[1, -1, 0, 334683, -148125659]$$ $$363979050334199/1041836936400$$ $$-11867173853681250000$$ $$$$ $$2949120$$ $$2.3435$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 169650.2.a.dy

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} + 4 q^{11} + q^{13} + q^{16} - 4 q^{17} + O(q^{20})$$ 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 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. 