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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-128.1-b
• 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-b over \(\Q(\sqrt{17}) \)

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

Curve label	Weierstrass Coefficients
128.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -37 a + 97\) , \( 38 a - 98\bigr] \)
128.1-b2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 533 a - 1364\) , \( -10078 a + 25816\bigr] \)
128.1-b3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 33 a - 84\) , \( -178 a + 456\bigr] \)
128.1-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 4\) , \( -2 a - 4\bigr] \)
128.1-b5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -28 a - 43\) , \( 142 a + 222\bigr] \)
128.1-b6	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a - 84\) , \( -218 a - 388\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph