Elliptic curve isogeny class 81225.1-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.1-e
• Conductor: 81225.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 81225.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
81225.1-e1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3663 a + 6648\) , \( 125748 a + 67671\bigr] \)
81225.1-e2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 42 a + 93\) , \( -492 a + 516\bigr] \)
81225.1-e3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -573 a - 792\) , \( 19482 a + 969\bigr] \)
81225.1-e4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -198 a + 408\) , \( 1737 a + 1584\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph