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

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

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

Curve label	Weierstrass Coefficients
96.1-c1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 12\) , \( 2 a + 16\bigr] \)
96.1-c2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 50243 a - 87026\) , \( 8070189 a - 13977979\bigr] \)
96.1-c3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 920 a - 1591\) , \( 18385 a - 31843\bigr] \)
96.1-c4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3102 a + 5373\) , \( 535777 a - 927993\bigr] \)
96.1-c5	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 55 a - 91\) , \( -260 a + 452\bigr] \)
96.1-c6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -110 a + 194\) , \( -1310 a + 2270\bigr] \)

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