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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-256.1-d
• 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-d over \(\Q(\sqrt{17}) \)

Isogeny class 256.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.1-d1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -38 a - 77\) , \( 268 a + 444\bigr] \)
256.1-d2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
256.1-d3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4\) , \( -a + 4\bigr] \)
256.1-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 40 a - 116\) , \( -229 a + 596\bigr] \)

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