Elliptic curve isogeny class 16.5-a over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-16.5-a
• Conductor: 16.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{209}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).

Elliptic curves in class 16.5-a over \(\Q(\sqrt{209}) \)

Isogeny class 16.5-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
16.5-a1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -931337 a - 6266403\) , \( -1351685915 a - 9094705362\bigr] \)
16.5-a2	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 317 a - 2430\) , \( -7754 a + 59890\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph