Elliptic curve isogeny class 120000.1-h over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-120000.1-h
• Conductor: 120000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 120000.1-h over \(\Q(\sqrt{-3}) \)

Isogeny class 120000.1-h contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
120000.1-h1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 125 a + 142\) , \( -1125 a + 1538\bigr] \)
120000.1-h2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -125 a + 267\) , \( 1125 a + 413\bigr] \)
120000.1-h3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 392\) , \( -21712\bigr] \)
120000.1-h4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \)
120000.1-h5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -108\) , \( 288\bigr] \)
120000.1-h6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -608\) , \( -5712\bigr] \)
120000.1-h7	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1608\) , \( 24288\bigr] \)
120000.1-h8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -9608\) , \( -365712\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph