Elliptic curve isogeny class 324.1-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-324.1-b
• Conductor: 324.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.1-b over \(\Q(\sqrt{17}) \)

Isogeny class 324.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
324.1-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 a - 56\) , \( -162 a - 269\bigr] \)
324.1-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a + 4\) , \( 2 a + 3\bigr] \)
324.1-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a + 7\) , \( -2 a + 5\bigr] \)
324.1-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 a - 83\) , \( 162 a - 431\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph