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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-120000.1-c
• Conductor: 120000.1
• Rank: \( 2 \)

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

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

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

Isogeny class 120000.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
120000.1-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2008\) , \( -295988\bigr] \)
120000.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1992\) , \( 6012\bigr] \)
120000.1-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -508\) , \( 1012\bigr] \)
120000.1-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5008\) , \( -133988\bigr] \)
120000.1-c5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -383\) , \( 3012\bigr] \)
120000.1-c6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -80008\) , \( -8683988\bigr] \)

Rank

Rank: \( 2 \)

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