Elliptic curve isogeny class 100048.4-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-100048.4-a
• Conductor: 100048.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 100048.4-a over \(\Q(\sqrt{-3}) \)

Isogeny class 100048.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100048.4-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -273 a + 13\) , \( 2020 a - 1168\bigr] \)
100048.4-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -473 a + 733\) , \( 6700 a + 3740\bigr] \)
100048.4-a3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -238 a + 53\) , \( 2835 a - 1154\bigr] \)
100048.4-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8038 a + 13333\) , \( 316475 a + 234302\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph