Elliptic curve isogeny class 28224.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-28224.2-c
• Conductor: 28224.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 28224.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 28224.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28224.2-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 21\) , \( 84 a + 30\bigr] \)
28224.2-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a + 24\) , \( -84 a + 114\bigr] \)
28224.2-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 9\bigr] \)
28224.2-c4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 450\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph