Elliptic curve isogeny class 2166.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2166.1-a
• Conductor: 2166.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 2166.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 2166.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2166.1-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -418\) , \( 3610\bigr] \)
2166.1-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 32\) , \( -8\bigr] \)
2166.1-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -8\) , \( 0\bigr] \)
2166.1-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -428\) , \( 3444\bigr] \)

Rank

Rank: \( 1 \)

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