Elliptic curve isogeny class 132.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-132.1-a
• Conductor: 132.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 132.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 132.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
132.1-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 1188 a - 2090\) , \( -29886 a + 51882\bigr] \)
132.1-a2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 18 a - 20\) , \( -42 a + 78\bigr] \)
132.1-a3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 58 a - 150\) , \( -512 a + 882\bigr] \)
132.1-a4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a\) , \( 0\bigr] \)
132.1-a5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 16\) , \( 18 a + 31\bigr] \)
132.1-a6	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 63 a - 150\) , \( -462 a + 858\bigr] \)
132.1-a7	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -12 a\) , \( -24 a - 54\bigr] \)
132.1-a8	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -770 a - 1336\) , \( 15138 a + 26227\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\ 3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\ 4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\ 6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\ 12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\ 2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\ 12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\ 4 & 12 & 4 & 6 & 3 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph