Elliptic curve isogeny class 71148.2-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-71148.2-g
• Conductor: 71148.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 71148.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 71148.2-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
71148.2-g1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -823 a + 823\) , \( -11611\bigr] \)
71148.2-g2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 77 a - 77\) , \( 161\bigr] \)
71148.2-g3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -363 a + 363\) , \( 1305\bigr] \)
71148.2-g4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -14133 a + 14133\) , \( -647829\bigr] \)

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