Elliptic curve isogeny class 100156.4-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100156.4-c
• Conductor: 100156.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 100156.4-c over \(\Q(\sqrt{-3}) \)

Isogeny class 100156.4-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100156.4-c1	\( \bigl[1\) , \( a\) , \( 1\) , \( 51 a - 700\) , \( -839 a + 6937\bigr] \)
100156.4-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -777 a - 1015\) , \( 22687 a + 5929\bigr] \)
100156.4-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 203 a - 525\) , \( 2793 a - 4361\bigr] \)
100156.4-c4	\( \bigl[1\) , \( a\) , \( 1\) , \( 611 a - 1540\) , \( 13161 a - 12103\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph