Elliptic curve isogeny class 8112.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8112.2-b
• Conductor: 8112.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 8112.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 8112.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
8112.2-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -13 a + 13\) , \( -4\bigr] \)
8112.2-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -748 a + 748\) , \( -7564\bigr] \)
8112.2-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -148 a + 148\) , \( 644\bigr] \)
8112.2-b4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -733 a + 733\) , \( -7888\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph