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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-324.1-c
• 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-c over \(\Q(\sqrt{17}) \)

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

Curve label	Weierstrass Coefficients
324.1-c1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a - 110\) , \( -777 a - 1215\bigr] \)
324.1-c2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a + 10\) , \( 18 a + 29\bigr] \)
324.1-c3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a - 20\) , \( -32 a + 79\bigr] \)
324.1-c4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -68 a + 160\) , \( 573 a - 1485\bigr] \)

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