Elliptic curve isogeny class 96.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-96.1-b
• Conductor: 96.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 96.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 96.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
96.1-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 97256 a - 168452\) , \( 21662226 a - 37520076\bigr] \)
96.1-b2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 9135 a - 15826\) , \( -619924 a + 1073738\bigr] \)
96.1-b3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 570 a - 991\) , \( -9409 a + 16295\bigr] \)
96.1-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2720 a - 4711\) , \( -10125 a + 17537\bigr] \)
96.1-b5	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 12\) , \( -3 a + 16\bigr] \)
96.1-b6	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -37569 a + 65072\) , \( -632444 a + 1095425\bigr] \)

Rank

Rank: \( 0 \)

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