Elliptic curve isogeny class 81225.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-81225.2-a
• Conductor: 81225.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 81225.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 81225.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
81225.2-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 147 a - 390\) , \( 1444 a - 2658\bigr] \)
81225.2-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -18 a\) , \( 37 a - 12\bigr] \)
81225.2-a3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -3 a - 15\) , \( 64 a - 63\bigr] \)
81225.2-a4	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 87 a + 120\) , \( 712 a - 972\bigr] \)

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