Elliptic curve isogeny class 400.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-400.1-a
• Conductor: 400.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 400.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 400.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
400.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -36 a + 36\) , \( -140\bigr] \)
400.1-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( 4\bigr] \)
400.1-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
400.1-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -41 a + 41\) , \( -116\bigr] \)

Rank

Rank: \( 0 \)

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