Elliptic curve isogeny class 64.1-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-64.1-b
• Conductor: 64.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 64.1-b over \(\Q(\sqrt{17}) \)

Isogeny class 64.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
64.1-b1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -267 a - 420\) , \( -7254 a - 11336\bigr] \)
64.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 2\) , \( -a + 1\bigr] \)
64.1-b3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -27 a - 40\) , \( -26 a - 40\bigr] \)
64.1-b4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a\) , \( a\bigr] \)
64.1-b5	\( \bigl[0\) , \( a\) , \( 0\) , \( 347 a - 887\) , \( 4862 a - 12454\bigr] \)
64.1-b6	\( \bigl[0\) , \( a\) , \( 0\) , \( 267 a - 687\) , \( 7254 a - 18590\bigr] \)

Rank

Rank: \( 0 \)

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