Elliptic curve isogeny class 106875.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-106875.1-a
• Conductor: 106875.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 106875.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 106875.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
106875.1-a1	\( \bigl[1\) , \( -1\) , \( a\) , \( -113 a - 117\) , \( 1106 a + 260\bigr] \)
106875.1-a2	\( \bigl[1\) , \( -1\) , \( a\) , \( -488 a + 633\) , \( 1856 a + 6635\bigr] \)
106875.1-a3	\( \bigl[1\) , \( -1\) , \( a\) , \( 12 a + 8\) , \( -19 a + 10\bigr] \)
106875.1-a4	\( \bigl[1\) , \( -1\) , \( a\) , \( 137 a + 133\) , \( -1144 a + 1510\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph