Elliptic curve isogeny class 512.2-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-512.2-b
• Conductor: 512.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 512.2-b over \(\Q(\sqrt{17}) \)

Isogeny class 512.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
512.2-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 136 a - 344\) , \( -1200 a + 3072\bigr] \)
512.2-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 24\) , \( -10 a + 24\bigr] \)
512.2-b3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
512.2-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 81 a - 204\) , \( 568 a - 1456\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph