Elliptic curve isogeny class 81225.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.2-b
• Conductor: 81225.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 81225.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
81225.2-b1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 16 a - 17\) , \( -38 a + 26\bigr] \)
81225.2-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( a - 17\) , \( -65 a + 2\bigr] \)
81225.2-b3	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -89 a + 208\) , \( -713 a - 259\bigr] \)
81225.2-b4	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -149 a - 242\) , \( -1445 a - 1213\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph