Elliptic curve isogeny class 28899.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-28899.1-d
• Conductor: 28899.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 28899.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 28899.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
28899.1-d1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 106\) , \( 525 a - 306\bigr] \)
28899.1-d2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 339 a - 224\) , \( 2607 a + 480\bigr] \)
28899.1-d3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -a - 9\) , \( -3 a + 8\bigr] \)
28899.1-d4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 4 a - 124\) , \( -27 a + 560\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph