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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.7-n
• Conductor: 576.7
• Rank: \( 1 \)

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

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

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

Isogeny class 576.7-n contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
576.7-n1	\( \bigl[a\) , \( 1\) , \( a\) , \( 21 a - 61\) , \( 93 a - 253\bigr] \)
576.7-n2	\( \bigl[a\) , \( -1\) , \( a\) , \( 34 a - 9\) , \( 701 a + 1285\bigr] \)
576.7-n3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a + 75\) , \( -100 a + 257\bigr] \)
576.7-n4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 10 a - 25\) , \( -25 a + 61\bigr] \)
576.7-n5	\( \bigl[a\) , \( -1\) , \( a\) , \( -41 a - 69\) , \( 191 a + 301\bigr] \)
576.7-n6	\( \bigl[a\) , \( a\) , \( a\) , \( -268 a - 420\) , \( -3824 a - 5972\bigr] \)
576.7-n7	\( \bigl[a\) , \( a\) , \( a\) , \( 22 a - 60\) , \( -124 a + 316\bigr] \)
576.7-n8	\( \bigl[a\) , \( -1\) , \( a\) , \( -296 a + 751\) , \( 43001 a - 110155\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph