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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-f
• 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-f over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
37632.2-f1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 7520 a - 2384\) , \( 119424 a + 121984\bigr] \)
37632.2-f2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -544\) , \( 13888\bigr] \)
37632.2-f3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( 0\bigr] \)
37632.2-f4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \)
37632.2-f5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7520 a + 5136\) , \( -119424 a + 241408\bigr] \)
37632.2-f6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -5760\bigr] \)
37632.2-f7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -784\) , \( 8704\bigr] \)
37632.2-f8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12544\) , \( 544960\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 16 & 8 & 4 & 16 & 4 & 8 \\ 2 & 1 & 8 & 4 & 2 & 8 & 2 & 4 \\ 16 & 8 & 1 & 2 & 16 & 4 & 4 & 8 \\ 8 & 4 & 2 & 1 & 8 & 2 & 2 & 4 \\ 4 & 2 & 16 & 8 & 1 & 16 & 4 & 8 \\ 16 & 8 & 4 & 2 & 16 & 1 & 4 & 8 \\ 4 & 2 & 4 & 2 & 4 & 4 & 1 & 2 \\ 8 & 4 & 8 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph