Elliptic curve isogeny class 100009.9-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100009.9-d
• Conductor: 100009.9
• Rank: \( 0 \)

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

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

Elliptic curves in class 100009.9-d over \(\Q(\sqrt{-3}) \)

Isogeny class 100009.9-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100009.9-d1	\( \bigl[1\) , \( -a\) , \( 1\) , \( -19 a + 37\) , \( 62 a + 9\bigr] \)
100009.9-d2	\( \bigl[1\) , \( -a\) , \( 1\) , \( 6 a - 3\) , \( 2 a + 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph