Elliptic curve isogeny class 1089.1-k over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1089.1-k
• Conductor: 1089.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1089.1-k over \(\Q(\sqrt{3}) \)

Isogeny class 1089.1-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1089.1-k1	\( \bigl[a\) , \( 0\) , \( a\) , \( 75 a - 138\) , \( 486 a - 901\bigr] \)
1089.1-k2	\( \bigl[a\) , \( 0\) , \( a\) , \( -3\) , \( -1\bigr] \)
1089.1-k3	\( \bigl[a\) , \( 0\) , \( a\) , \( -18\) , \( -31\bigr] \)
1089.1-k4	\( \bigl[a\) , \( 0\) , \( a\) , \( -75 a - 138\) , \( -486 a - 901\bigr] \)

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