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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-96.1-d
• 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-d over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
96.1-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 97256 a - 168452\) , \( -21662226 a + 37520076\bigr] \)
96.1-d2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 9137 a - 15823\) , \( 629060 a - 1089563\bigr] \)
96.1-d3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 572 a - 988\) , \( 9980 a - 17285\bigr] \)
96.1-d4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2720 a - 4711\) , \( 10125 a - 17537\bigr] \)
96.1-d5	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -3 a - 9\) , \( -27\bigr] \)
96.1-d6	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -37568 a + 65073\) , \( 659947 a - 1143060\bigr] \)

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