Elliptic curve isogeny class 81225.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.3-e
• Conductor: 81225.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 81225.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.3-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
81225.3-e1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 2985 a - 6648\) , \( -125748 a + 193419\bigr] \)
81225.3-e2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 210 a - 408\) , \( -1737 a + 3321\bigr] \)
81225.3-e3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 135 a - 93\) , \( 492 a + 24\bigr] \)
81225.3-e4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1365 a + 792\) , \( -19482 a + 20451\bigr] \)

Rank

Rank: \( 1 \)

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