Elliptic curve isogeny class 1344.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-1344.2-b
• Conductor: 1344.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1344.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 1344.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1344.2-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a - 3\) , \( 35 a - 14\bigr] \)
1344.2-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a + 2\) , \( -3 a - 15\bigr] \)
1344.2-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -34 a + 37\) , \( 47 a + 82\bigr] \)
1344.2-b4	\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 3\) , \( 2 a - 2\bigr] \)
1344.2-b5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 48\) , \( 68 a - 116\bigr] \)
1344.2-b6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -234 a - 43\) , \( 1895 a - 638\bigr] \)