Elliptic curve isogeny class 900.1-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-b
• Conductor: 900.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 900.1-b over \(\Q(\sqrt{17}) \)

Isogeny class 900.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
900.1-b1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -203 a - 320\) , \( 7036 a + 10984\bigr] \)
900.1-b2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 624 a + 956\) , \( 1120 a + 1776\bigr] \)
900.1-b3	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -156 a - 244\) , \( 400 a + 624\bigr] \)
900.1-b4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -33 a + 73\) , \( -93 a + 197\bigr] \)
900.1-b5	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 13 a - 81\) , \( 101 a - 163\bigr] \)
900.1-b6	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -187 a - 281\) , \( 2141 a + 2117\bigr] \)

Rank

Rank: \( 1 \)

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