Elliptic curve isogeny class 100044.4-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100044.4-c
• Conductor: 100044.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 100044.4-c over \(\Q(\sqrt{-3}) \)

Isogeny class 100044.4-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100044.4-c1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1032 a - 2595\) , \( 26973 a - 47925\bigr] \)
100044.4-c2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -328 a - 355\) , \( 4205 a + 1947\bigr] \)
100044.4-c3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 35\) , \( 109 a - 37\bigr] \)
100044.4-c4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 912 a - 2535\) , \( 31473 a - 49365\bigr] \)

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