Elliptic curve isogeny class 100044.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100044.1-c
• Conductor: 100044.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 100044.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 100044.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100044.1-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1563 a + 2595\) , \( -26973 a - 20952\bigr] \)
100044.1-c2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -683 a + 355\) , \( -4205 a + 6152\bigr] \)
100044.1-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1623 a + 2535\) , \( -31473 a - 17892\bigr] \)
100044.1-c4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -43 a + 35\) , \( -109 a + 72\bigr] \)

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