Elliptic curve isogeny class 100156.3-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100156.3-d
• Conductor: 100156.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 100156.3-d over \(\Q(\sqrt{-3}) \)

Isogeny class 100156.3-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100156.3-d1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 190 a - 523\) , \( 1947 a - 4408\bigr] \)
100156.3-d2	\( \bigl[1\) , \( a\) , \( 1\) , \( 989 a + 539\) , \( 309 a - 12817\bigr] \)
100156.3-d3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 1680 a - 1393\) , \( -27587 a + 3136\bigr] \)
100156.3-d4	\( \bigl[1\) , \( a\) , \( 1\) , \( 269 a + 499\) , \( -6491 a + 6623\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph