Elliptic curve isogeny class 9.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-9.1-a
• Conductor: 9.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 9.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 9.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 48 a - 123\) , \( 291 a - 749\bigr] \)
9.1-a2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 32 a - 79\) , \( -131 a + 330\bigr] \)
9.1-a3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 58 a + 92\) , \( 322 a + 503\bigr] \)
9.1-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -22 a - 33\) , \( 71 a + 111\bigr] \)
9.1-a5	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a - 4\) , \( -2 a + 3\bigr] \)
9.1-a6	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -a - 2\) , \( -1\bigr] \)
9.1-a7	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -49 a - 74\) , \( -292 a - 457\bigr] \)
9.1-a8	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -31 a - 47\) , \( 99 a + 152\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph