Elliptic curve isogeny class 100156.5-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100156.5-c
• Conductor: 100156.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 100156.5-c over \(\Q(\sqrt{-3}) \)

Isogeny class 100156.5-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100156.5-c1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 525 a - 203\) , \( -2793 a - 1568\bigr] \)
100156.5-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -929 a + 1539\) , \( -13161 a + 1058\bigr] \)
100156.5-c3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1015 a + 777\) , \( -22687 a + 28616\bigr] \)
100156.5-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -649 a + 699\) , \( 839 a + 6098\bigr] \)

Rank

Rank: \( 1 \)

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