Elliptic curve isogeny class 28899.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-28899.2-c
• Conductor: 28899.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 28899.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 28899.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
28899.2-c1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -118 a - 7\) , \( 564 a - 231\bigr] \)
28899.2-c2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -243 a + 333\) , \( 1743 a + 1720\bigr] \)
28899.2-c3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 102 a + 3\) , \( -54 a + 463\bigr] \)
28899.2-c4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 2\) , \( 3 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph