Elliptic curve isogeny class 100044.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100044.1-a
• Conductor: 100044.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100044.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 100044.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
100044.1-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -28 a + 8\) , \( -763 a + 530\bigr] \)
100044.1-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2 a + 8\) , \( 5 a - 10\bigr] \)
100044.1-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2 a + 68\) , \( -259 a + 110\bigr] \)
100044.1-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 32 a + 1088\) , \( -16411 a + 8330\bigr] \)

Rank

Rank: \( 1 \)

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