Elliptic curve isogeny class 144.4-d over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-144.4-d
• Conductor: 144.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.4-d over \(\Q(\sqrt{17}) \)

Isogeny class 144.4-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.4-d1	\( \bigl[a\) , \( a\) , \( 0\) , \( 741 a - 1903\) , \( -16047 a + 41078\bigr] \)
144.4-d2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 6 a + 8\) , \( -33 a - 52\bigr] \)
144.4-d3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a - 8\) , \( 5 a + 8\bigr] \)
144.4-d4	\( \bigl[a\) , \( a\) , \( 0\) , \( 11 a - 23\) , \( 17 a - 42\bigr] \)
144.4-d5	\( \bigl[a\) , \( a\) , \( 0\) , \( 46 a - 123\) , \( -258 a + 634\bigr] \)
144.4-d6	\( \bigl[a\) , \( a\) , \( 0\) , \( -89 a + 57\) , \( -1329 a + 2254\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph