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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-57600.1-b
• 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-b over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
57600.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 39 a\) , \( 204 a - 102\bigr] \)
57600.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a\) , \( 36 a - 18\bigr] \)
57600.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a\) , \( -6 a + 3\bigr] \)
57600.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -321 a\) , \( 2556 a - 1278\bigr] \)

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