Elliptic curve isogeny class 25921.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-25921.2-a
• Conductor: 25921.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 25921.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 25921.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25921.2-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 26 a - 27\) , \( 36\bigr] \)
25921.2-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -9 a + 8\) , \( 8\bigr] \)
25921.2-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -4 a + 3\) , \( -2\bigr] \)
25921.2-a4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -124 a + 123\) , \( 560\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph