Elliptic curve isogeny class 256.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-256.1-a
• Conductor: 256.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 256.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
256.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( -27 a - 42\bigr] \)
256.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 32 a + 34\bigr] \)
256.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 7\) , \( 4 a + 6\bigr] \)
256.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 11\) , \( -4 a + 10\bigr] \)
256.1-a5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 27 a - 69\bigr] \)
256.1-a6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 29\) , \( -32 a + 66\bigr] \)

Rank

Rank: \( 0 \)

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