Elliptic curve isogeny class 576.7-h over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.7-h
• Conductor: 576.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 576.7-h over \(\Q(\sqrt{17}) \)

Isogeny class 576.7-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.7-h1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 90 a - 449\) , \( 1584 a - 3029\bigr] \)
576.7-h2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 116 a + 183\) , \( 3260 a + 5091\bigr] \)
576.7-h3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -103 a + 264\) , \( -1446 a + 3704\bigr] \)
576.7-h4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9\) , \( -2 a + 3\bigr] \)
576.7-h5	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -45 a - 109\) , \( 250 a + 307\bigr] \)
576.7-h6	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -900 a - 1369\) , \( 19384 a + 29899\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph