Elliptic curve isogeny class 256.4-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-256.4-a
• Conductor: 256.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.4-a over \(\Q(\sqrt{17}) \)

Isogeny class 256.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.4-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 41 a - 161\) , \( 369 a - 801\bigr] \)
256.4-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \)
256.4-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a + 31\) , \( 73 a - 187\bigr] \)
256.4-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 548 a - 1409\) , \( 9901 a - 25355\bigr] \)

Rank

Rank: \( 0 \)

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