Elliptic curve isogeny class 100009.7-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100009.7-b
• Conductor: 100009.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 100009.7-b over \(\Q(\sqrt{-3}) \)

Isogeny class 100009.7-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
100009.7-b1	\( \bigl[0\) , \( 1\) , \( a\) , \( -84 a + 128\) , \( -289 a - 226\bigr] \)
100009.7-b2	\( \bigl[0\) , \( 1\) , \( a\) , \( -14 a + 238\) , \( 1384 a - 1237\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph