Elliptic curve isogeny class 272.4-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-272.4-a
• Conductor: 272.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 272.4-a over \(\Q(\sqrt{17}) \)

Isogeny class 272.4-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
272.4-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2257 a - 5996\) , \( 87789 a - 223905\bigr] \)
272.4-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a - 1\) , \( 70 a - 126\bigr] \)
272.4-a3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 16 a + 25\) , \( 0\bigr] \)
272.4-a4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a - 1\) , \( 0\bigr] \)
272.4-a5	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 7 a - 26\) , \( 25 a - 61\bigr] \)
272.4-a6	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -38 a + 103\) , \( -106 a + 274\bigr] \)
272.4-a7	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 92 a - 451\) , \( 1640 a - 3240\bigr] \)
272.4-a8	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -713 a - 1706\) , \( 19871 a + 25189\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph