Elliptic curve isogeny class 6400.1-h over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-6400.1-h
• Conductor: 6400.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 6400.1-h over \(\Q(\sqrt{-3}) \)

Isogeny class 6400.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
6400.1-h1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \)
6400.1-h2	\( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 4\) , \( -4\bigr] \)
6400.1-h3	\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \)
6400.1-h4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)

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