Properties

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

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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 \([1, -1, 0, -187317, -26499659]\) \(63812982460681/10201800960\) \(116204889060000000\) \([2]\) \(1474560\) \(1.9969\) \(\Gamma_0(N)\)-optimal
169650.bo2 169650dy2 \([1, -1, 0, 334683, -148125659]\) \(363979050334199/1041836936400\) \(-11867173853681250000\) \([2]\) \(2949120\) \(2.3435\)  

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)
 
\(q - q^{2} + q^{4} - q^{8} + 4 q^{11} + q^{13} + q^{16} - 4 q^{17} + O(q^{20})\)  Toggle raw display

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.