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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2166.1-e
• 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-e over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
2166.1-e1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5312\) , \( -167551\bigr] \)
2166.1-e2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2431\bigr] \)
2166.1-e3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5472\) , \( -158079\bigr] \)
2166.1-e4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -87552\) , \( -10007679\bigr] \)

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