Elliptic curve isogeny class 57600.1-j over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-57600.1-j
• Conductor: 57600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 57600.1-j over \(\Q(\sqrt{-3}) \)

Isogeny class 57600.1-j contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
57600.1-j1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5280 a\) , \( -316728 a + 158364\bigr] \)
57600.1-j2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 0\) , \( 72 a - 36\bigr] \)
57600.1-j3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1680 a\) , \( -17400 a + 8700\bigr] \)
57600.1-j4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -480 a\) , \( -1848 a + 924\bigr] \)
57600.1-j5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -240 a\) , \( 1800 a - 900\bigr] \)
57600.1-j6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6480 a\) , \( -227448 a + 113724\bigr] \)
57600.1-j7	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3840 a\) , \( 108360 a - 54180\bigr] \)
57600.1-j8	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -103680 a\) , \( -14768568 a + 7384284\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph