Elliptic curve isogeny class 57600.1-q over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-57600.1-q
• Conductor: 57600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 57600.1-q over \(\Q(\sqrt{-3}) \)

Isogeny class 57600.1-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
57600.1-q1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -204 a + 102\bigr] \)
57600.1-q2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 21\) , \( -36 a + 18\bigr] \)
57600.1-q3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 6 a - 3\bigr] \)
57600.1-q4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 321\) , \( -2556 a + 1278\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph