Elliptic curve isogeny class 102400.1-h over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-102400.1-h
• Conductor: 102400.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 102400.1-h over \(\Q(\sqrt{-3}) \)

Isogeny class 102400.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
102400.1-h1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -163 a\) , \( -954 a + 477\bigr] \)
102400.1-h2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -123 a + 124\) , \( -126 a + 1\bigr] \)
102400.1-h3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 517 a - 516\) , \( -1534 a + 1025\bigr] \)
102400.1-h4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2723 a\) , \( -61370 a + 30685\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph