Elliptic curve isogeny class 16900.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-16900.2-a
• Conductor: 16900.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 16900.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 16900.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
16900.2-a1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 12 a\) , \( 156\bigr] \)
16900.2-a2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -113 a\) , \( -4194\bigr] \)
16900.2-a3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 207 a\) , \( -1122\bigr] \)
16900.2-a4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 32 a\) , \( 68\bigr] \)

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