Elliptic curve isogeny class 144.1-j over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-144.1-j
• Conductor: 144.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 144.1-j over \(\Q(\sqrt{22}) \)

Isogeny class 144.1-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.1-j1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -64813 a + 304010\) , \( -142529688 a + 668523501\bigr] \)
144.1-j2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
144.1-j3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 17927 a - 84075\) , \( 2145787 a - 10064627\bigr] \)
144.1-j4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 100667 a - 472160\) , \( -35735098 a + 167612473\bigr] \)
144.1-j5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -266147 a - 1248330\) , \( -162337672 a - 761431169\bigr] \)
144.1-j6	\( \bigl[a\) , \( 0\) , \( 0\) , \( 1589987 a - 7457690\) , \( -2360598268 a + 11072187325\bigr] \)

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