Elliptic curve isogeny class 10000.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-10000.1-a
• Conductor: 10000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 10000.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 10000.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10000.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -908\) , \( -15688\bigr] \)
10000.1-a2	\( \bigl[0\) , \( a\) , \( 0\) , \( 92 a - 92\) , \( 312\bigr] \)
10000.1-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -33 a + 33\) , \( 62\bigr] \)
10000.1-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \)

Rank

Rank: \( 1 \)

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