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

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

Isogeny class 57600.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57600.1-h1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 242 a - 241\) , \( 14159 a - 6959\bigr] \)
57600.1-h2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -238 a + 239\) , \( -241 a + 1\bigr] \)
57600.1-h3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 62 a - 61\) , \( -61 a + 61\bigr] \)
57600.1-h4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 602 a - 601\) , \( 6311 a - 2855\bigr] \)
57600.1-h5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 47 a - 46\) , \( -154 a + 100\bigr] \)
57600.1-h6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9602 a - 9601\) , \( 414911 a - 202655\bigr] \)

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