Elliptic curve isogeny class 37632.3-j over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.3-j
• Conductor: 37632.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 37632.3-j over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.3-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
37632.3-j1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 18 a + 285\) , \( 2139 a - 1266\bigr] \)
37632.3-j2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 123 a - 30\) , \( 165 a + 393\bigr] \)
37632.3-j3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 20\) , \( 360 a - 360\bigr] \)
37632.3-j4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 163 a - 290\) , \( -1591 a + 2693\bigr] \)
37632.3-j5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 15\) , \( 36 a - 18\bigr] \)
37632.3-j6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2003 a - 490\) , \( 11377 a + 22477\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph