Elliptic curve isogeny class 100009.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100009.1-a
• Conductor: 100009.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 100009.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 100009.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100009.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 27 a + 10\) , \( -42 a + 88\bigr] \)
100009.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 5\) , \( -7 a + 11\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph