Elliptic curve isogeny class 512.1-d over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-512.1-d
• Conductor: 512.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 512.1-d over \(\Q(\sqrt{17}) \)

Isogeny class 512.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
512.1-d1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 4\) , \( -2 a - 4\bigr] \)
512.1-d2	\( \bigl[0\) , \( a\) , \( 0\) , \( 9 a - 21\) , \( 8 a - 20\bigr] \)
512.1-d3	\( \bigl[0\) , \( a\) , \( 0\) , \( 124 a - 316\) , \( 1012 a - 2592\bigr] \)
512.1-d4	\( \bigl[0\) , \( a\) , \( 0\) , \( 59 a - 151\) , \( -378 a + 966\bigr] \)

Rank

Rank: \( 0 \)

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