Elliptic curve isogeny class 144.5-d over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-144.5-d
• Conductor: 144.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.5-d over \(\Q(\sqrt{17}) \)

Isogeny class 144.5-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.5-d1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 94 a - 30\) , \( 1387 a + 1289\bigr] \)
144.5-d2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 6 a - 14\) , \( -5 a + 13\bigr] \)
144.5-d3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -6 a - 10\) , \( -39 a - 61\bigr] \)
144.5-d4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -41 a - 75\) , \( 136 a + 200\bigr] \)
144.5-d5	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -6 a + 14\) , \( 33 a - 85\bigr] \)
144.5-d6	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -736 a - 1160\) , \( 14145 a + 22075\bigr] \)

Rank

Rank: \( 1 \)

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