Elliptic curve isogeny class 1083.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1083.1-b
• Conductor: 1083.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1083.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 1083.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1083.1-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( -30\bigr] \)
1083.1-b2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 86 a - 146\) , \( -500 a + 867\bigr] \)
1083.1-b3	\( \bigl[a\) , \( -1\) , \( a\) , \( -8\) , \( -6\bigr] \)
1083.1-b4	\( \bigl[a\) , \( -1\) , \( a\) , \( -103\) , \( -386\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph