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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2166.1-b
• Conductor: 2166.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2166.1-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -5311\) , \( 162239\bigr] \)
2166.1-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -351\) , \( 2079\bigr] \)
2166.1-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -5471\) , \( 152607\bigr] \)
2166.1-b4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -87551\) , \( 9920127\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph