Elliptic curve isogeny class 16.1-a over number field \(\Q(\sqrt{201}) \)

• Base field: \(\Q(\sqrt{201}) \)
• Label: 2.2.201.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{201}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 50 \); class number \(1\).

Elliptic curves in class 16.1-a over \(\Q(\sqrt{201}) \)

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 17\) , \( 14193713 a - 107712186\bigr] \)
16.1-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 17\) , \( -14193713 a - 93518456\bigr] \)
16.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 363321 a - 2757118\) , \( 312938562 a - 2374804224\bigr] \)
16.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -363319 a - 2393798\) , \( -313301882 a - 2064259460\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph