Elliptic curve isogeny class 128.6-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-128.6-a
• Conductor: 128.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 128.6-a over \(\Q(\sqrt{17}) \)

Isogeny class 128.6-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
128.6-a1	\( \bigl[a\) , \( a\) , \( a\) , \( a\) , \( a\bigr] \)
128.6-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -99 a - 157\) , \( -460 a - 721\bigr] \)
128.6-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( -49 a - 77\) , \( 220 a + 343\bigr] \)
128.6-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -a - 8\) , \( a + 2\bigr] \)

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