Elliptic curve isogeny class 3087.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-3087.2-a
• Conductor: 3087.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 3087.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 3087.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
3087.2-a1	\( \bigl[1\) , \( a\) , \( 0\) , \( 3474 a + 6465\) , \( -321486 a + 306732\bigr] \)
3087.2-a2	\( \bigl[1\) , \( a\) , \( 0\) , \( 654 a - 9045\) , \( -19194 a + 323526\bigr] \)
3087.2-a3	\( \bigl[1\) , \( a\) , \( 0\) , \( -816 a + 510\) , \( -13020 a + 24087\bigr] \)
3087.2-a4	\( \bigl[1\) , \( a\) , \( 0\) , \( 24 a - 15\) , \( 0\bigr] \)
3087.2-a5	\( \bigl[1\) , \( a\) , \( 0\) , \( -96 a + 60\) , \( -60 a + 111\bigr] \)
3087.2-a6	\( \bigl[1\) , \( a\) , \( 0\) , \( -936 a + 585\) , \( 5400 a - 9990\bigr] \)
3087.2-a7	\( \bigl[1\) , \( a\) , \( 0\) , \( -1176 a + 735\) , \( -8160 a + 15096\bigr] \)
3087.2-a8	\( \bigl[1\) , \( a\) , \( 0\) , \( -18816 a + 11760\) , \( -510900 a + 945165\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph