Elliptic curve isogeny class 144.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-144.1-b
• Conductor: 144.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 144.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 144.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 34 a - 60\) , \( -126 a + 218\bigr] \)
144.1-b2	\( \bigl[0\) , \( a\) , \( 0\) , \( 34 a - 60\) , \( 126 a - 218\bigr] \)
144.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 9\) , \( 0\bigr] \)
144.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 9\) , \( 0\bigr] \)
144.1-b5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -34 a - 60\) , \( -126 a - 218\bigr] \)
144.1-b6	\( \bigl[0\) , \( a\) , \( 0\) , \( -34 a - 60\) , \( 126 a + 218\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 6 & 3 & 2 & 18 \\ 9 & 1 & 6 & 3 & 18 & 2 \\ 6 & 6 & 1 & 2 & 3 & 3 \\ 3 & 3 & 2 & 1 & 6 & 6 \\ 2 & 18 & 3 & 6 & 1 & 9 \\ 18 & 2 & 3 & 6 & 9 & 1 \end{array}\right)\)

Isogeny graph