Elliptic curve isogeny class 289.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-289.1-a
• Conductor: 289.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 289.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 289.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
289.1-a1	\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( 13\bigr] \)
289.1-a2	\( \bigl[a\) , \( 0\) , \( a\) , \( 7469 a - 12938\) , \( 199451 a - 345460\bigr] \)
289.1-a3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 318 a - 552\) , \( -4102 a + 7103\bigr] \)
289.1-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5078 a - 8797\) , \( -260547 a + 451279\bigr] \)

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