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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.3-a
• 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-a over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
81225.3-a1	\( \bigl[1\) , \( a\) , \( a\) , \( 5281 a + 1650\) , \( 142859 a - 409439\bigr] \)
81225.3-a2	\( \bigl[1\) , \( a\) , \( a\) , \( a\) , \( -31 a + 91\bigr] \)
81225.3-a3	\( \bigl[1\) , \( a\) , \( a\) , \( -1679 a - 525\) , \( 6248 a - 20216\bigr] \)
81225.3-a4	\( \bigl[1\) , \( a\) , \( a\) , \( 481 a + 150\) , \( 1199 a - 2909\bigr] \)
81225.3-a5	\( \bigl[1\) , \( a\) , \( a\) , \( 241 a + 75\) , \( -592 a + 2014\bigr] \)
81225.3-a6	\( \bigl[1\) , \( a\) , \( a\) , \( 6481 a + 2025\) , \( 104774 a - 297134\bigr] \)
81225.3-a7	\( \bigl[1\) , \( a\) , \( a\) , \( 3841 a + 1200\) , \( -44287 a + 133549\bigr] \)
81225.3-a8	\( \bigl[1\) , \( a\) , \( a\) , \( 103681 a + 32400\) , \( 6545489 a - 18926729\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph