Elliptic curve isogeny class 4800.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-4800.1-a
• Conductor: 4800.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4800.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 4800.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4800.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
4800.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
4800.1-a3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
4800.1-a4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
4800.1-a5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
4800.1-a6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph