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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-512.1-j
• 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-j over \(\Q(\sqrt{17}) \)

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

Curve label	Weierstrass Coefficients
512.1-j1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 97 a - 244\) , \( 752 a - 1928\bigr] \)
512.1-j2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6 a - 9\) , \( -7 a - 11\bigr] \)
512.1-j3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 7 a - 14\) , \( 12 a - 32\bigr] \)
512.1-j4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 44\) , \( -36 a + 100\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph