Elliptic curve isogeny class 532.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-532.3-b
• Conductor: 532.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 532.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 532.3-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
532.3-b1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -8 a - 81\) , \( -110 a - 241\bigr] \)
532.3-b2	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -a\) , \( -a\bigr] \)
532.3-b3	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 14 a - 5\) , \( -4 a - 13\bigr] \)
532.3-b4	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 194 a - 55\) , \( 512 a + 525\bigr] \)
532.3-b5	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1144 a - 455\) , \( -7470 a - 6371\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 3 & 9 & 9 \\ 9 & 1 & 3 & 9 & 9 \\ 3 & 3 & 1 & 3 & 3 \\ 9 & 9 & 3 & 1 & 9 \\ 9 & 9 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph