Elliptic curve isogeny class 37632.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-a
• Conductor: 37632.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 37632.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
37632.2-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -113\) , \( 516\bigr] \)
37632.2-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 15 a + 67\) , \( -285 a + 183\bigr] \)
37632.2-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -185 a - 13\) , \( -1525 a + 1535\bigr] \)
37632.2-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 185 a - 198\) , \( 1525 a + 10\bigr] \)
37632.2-a5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
37632.2-a6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -28\) , \( 28\bigr] \)
37632.2-a7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -15 a + 82\) , \( 285 a - 102\bigr] \)
37632.2-a8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1828\) , \( 30700\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph