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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-324.1-f
• Conductor: 324.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
324.1-f1	\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a - 12\) , \( 31 a + 48\bigr] \)
324.1-f2	\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a + 93\) , \( -574 a - 911\bigr] \)
324.1-f3	\( \bigl[1\) , \( -1\) , \( a\) , \( 67 a - 177\) , \( 776 a - 1991\bigr] \)
324.1-f4	\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a + 18\) , \( -19 a + 48\bigr] \)

Rank

Rank: \( 1 \)

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