Elliptic curve isogeny class 106875.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-106875.2-a
• Conductor: 106875.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 106875.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 106875.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
106875.2-a1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 269 a - 133\) , \( 1143 a + 366\bigr] \)
106875.2-a2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 144 a - 633\) , \( -1857 a + 8491\bigr] \)
106875.2-a3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -231 a + 117\) , \( -1107 a + 1366\bigr] \)
106875.2-a4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19 a - 8\) , \( 18 a - 9\bigr] \)

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