Elliptic curve isogeny class 100156.6-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100156.6-d
• Conductor: 100156.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 100156.6-d over \(\Q(\sqrt{-3}) \)

Isogeny class 100156.6-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100156.6-d1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -269 a + 768\) , \( 6491 a + 132\bigr] \)
100156.6-d2	\( \bigl[a\) , \( a\) , \( 0\) , \( 287 a + 1393\) , \( 27587 a - 24451\bigr] \)
100156.6-d3	\( \bigl[a\) , \( a\) , \( 0\) , \( -333 a + 523\) , \( -1947 a - 2461\bigr] \)
100156.6-d4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -989 a + 1528\) , \( -309 a - 12508\bigr] \)

Rank

Rank: \( 0 \)

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