Elliptic curve isogeny class 1089.2-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1089.2-a
• Conductor: 1089.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1089.2-a over \(\Q(\sqrt{3}) \)

Isogeny class 1089.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
1089.2-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 3816 a - 6611\) , \( 72469 a - 125520\bigr] \)
1089.2-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 383820452 a - 664796525\) , \( 5386969633888 a - 9330505104725\bigr] \)
1089.2-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 6889231 a - 11932502\) , \( 12956098743 a - 22440621292\bigr] \)
1089.2-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -253 a + 412\) , \( 1249 a - 2108\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph