Elliptic curve isogeny class 144.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-144.1-b
• Conductor: 144.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 144.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 144.1-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10 a + 27\) , \( 61 a - 161\bigr] \)
144.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a + 31\) , \( -34 a - 89\bigr] \)
144.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 a - 53\) , \( 22 a + 58\bigr] \)
144.1-b4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 9\) , \( -17 a - 44\bigr] \)
144.1-b5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -19 a - 69\) , \( 46 a + 181\bigr] \)
144.1-b6	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 5 a - 13\) , \( 4 a - 11\bigr] \)
144.1-b7	\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a - 53\) , \( -22 a + 58\bigr] \)
144.1-b8	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 20 a - 73\) , \( -119 a + 319\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\ 3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\ 4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\ 6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\ 12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\ 2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\ 12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\ 4 & 12 & 4 & 6 & 3 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph