Elliptic curve isogeny class 228.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-228.2-a
• Conductor: 228.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 228.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 228.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
228.2-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -140 a + 35\) , \( -615 a + 881\bigr] \)
228.2-a2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 0\) , \( a - 1\bigr] \)
228.2-a3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -167 a + 113\bigr] \)
228.2-a4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 10\) , \( 9 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph