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

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

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

Curve label	Weierstrass Coefficients
96.1-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a - 9\) , \( -27\bigr] \)
96.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 50243 a - 87023\) , \( -8019946 a + 13890954\bigr] \)
96.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 920 a - 1591\) , \( -18385 a + 31843\bigr] \)
96.1-a4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3102 a + 5373\) , \( -535777 a + 927993\bigr] \)
96.1-a5	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 56 a - 90\) , \( 222 a - 381\bigr] \)
96.1-a6	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -109 a + 195\) , \( 1392 a - 2409\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph