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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.6-k
• 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-k over \(\Q(\sqrt{17}) \)

Isogeny class 576.6-k contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.6-k1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 614 a + 903\) , \( 48002 a + 75106\bigr] \)
576.6-k2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 6 a + 2\) , \( 3 a + 1\bigr] \)
576.6-k3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -126 a - 197\) , \( -876 a - 1368\bigr] \)
576.6-k4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -601 a - 942\) , \( 10760 a + 16804\bigr] \)
576.6-k5	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -8 a - 3\) , \( -18 a + 4\bigr] \)
576.6-k6	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 3588 a - 9191\) , \( -184356 a + 472236\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph