Elliptic curve isogeny class 21609.3-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-21609.3-d
• Conductor: 21609.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 21609.3-d over \(\Q(\sqrt{-3}) \)

Isogeny class 21609.3-d contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
21609.3-d1	\( \bigl[1\) , \( -1\) , \( a\) , \( -53 a + 33\) , \( -79 a + 162\bigr] \)
21609.3-d2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -34 a + 53\) , \( 78 a + 83\bigr] \)
21609.3-d3	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -559 a + 893\) , \( 5013 a + 4535\bigr] \)
21609.3-d4	\( \bigl[1\) , \( -1\) , \( a\) , \( -893 a + 558\) , \( -5014 a + 9549\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 14 & 2 \\ 7 & 1 & 2 & 14 \\ 14 & 2 & 1 & 7 \\ 2 & 14 & 7 & 1 \end{array}\right)\)

Isogeny graph