Elliptic curve isogeny class 288.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-288.1-d
• Conductor: 288.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 288.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 288.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
288.1-d1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -79 a - 140\) , \( 1663 a + 2879\bigr] \)
288.1-d2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 10822 a - 18744\) , \( -809620 a + 1402303\bigr] \)
288.1-d3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 198 a - 342\) , \( -1746 a + 3024\bigr] \)
288.1-d4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -668 a + 1158\) , \( -54226 a + 93922\bigr] \)
288.1-d5	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 11 a - 21\) , \( 20 a - 34\bigr] \)
288.1-d6	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -34 a + 24\) , \( 164 a - 214\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph