Elliptic curve isogeny class 28812.3-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-28812.3-f
• Conductor: 28812.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 28812.3-f over \(\Q(\sqrt{-3}) \)

Isogeny class 28812.3-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
28812.3-f1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -197 a + 197\) , \( -2367\bigr] \)
28812.3-f2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 18913 a - 18913\) , \( -381333\bigr] \)
28812.3-f3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5097 a + 5097\) , \( -49995\bigr] \)
28812.3-f4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44787 a + 44787\) , \( 3609423\bigr] \)
28812.3-f5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4117 a + 4117\) , \( -101935\bigr] \)
28812.3-f6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65857 a + 65857\) , \( -6510547\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph