Elliptic curve isogeny class 64.4-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-64.4-b
• Conductor: 64.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 64.4-b over \(\Q(\sqrt{17}) \)

Isogeny class 64.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.4-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( -3 a + 6\bigr] \)
64.4-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 12\) , \( 3 a + 8\bigr] \)
64.4-b3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 2\) , \( -3 a - 4\bigr] \)
64.4-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -38 a - 57\) , \( -180 a - 281\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph