Elliptic curve isogeny class 128.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-128.1-a
• Conductor: 128.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 128.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 128.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
128.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 81 a - 220\) , \( -596 a + 1488\bigr] \)
128.1-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a + 25\) , \( 0\bigr] \)
128.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
128.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a + 40\) , \( -15 a + 40\bigr] \)
128.1-a5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 20\) , \( -12 a + 16\bigr] \)
128.1-a6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -79 a - 140\) , \( -516 a - 752\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph