Elliptic curve isogeny class 576.6-c over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.6-c
• Conductor: 576.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 576.6-c over \(\Q(\sqrt{17}) \)

Isogeny class 576.6-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.6-c1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 9 a - 22\) , \( -12 a + 31\bigr] \)
576.6-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -5 a - 8\) , \( 2 a + 3\bigr] \)
576.6-c3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 13 a - 30\) , \( 28 a - 71\bigr] \)
576.6-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -60 a - 93\) , \( 369 a + 576\bigr] \)

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