Elliptic curve isogeny class 64.6-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-64.6-b
• Conductor: 64.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 64.6-b over \(\Q(\sqrt{17}) \)

Isogeny class 64.6-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
64.6-b1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a + 13\) , \( 0\bigr] \)
64.6-b2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 68 a - 178\) , \( -469 a + 1200\bigr] \)
64.6-b3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 3 a - 13\) , \( -9 a + 20\bigr] \)
64.6-b4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 8\) , \( -16 a - 25\bigr] \)
64.6-b5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 13 a - 30\) , \( -534 a + 1369\bigr] \)
64.6-b6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -90 a - 143\) , \( -779 a - 1218\bigr] \)

Rank

Rank: \( 1 \)

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