Elliptic curve isogeny class 24.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-24.1-a
• Conductor: 24.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 24.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 24.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
24.1-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1035 a - 1791\) , \( -23450 a + 40617\bigr] \)
24.1-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -15 a + 29\) , \( 322 a - 557\bigr] \)
24.1-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 66\) , \( -168 a + 291\bigr] \)
24.1-a4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5 a - 6\) , \( -3 a + 6\bigr] \)
24.1-a5	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 25 a - 41\) , \( 92 a - 159\bigr] \)
24.1-a6	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 65 a - 111\) , \( -348 a + 603\bigr] \)
24.1-a7	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 385 a - 671\) , \( 5582 a - 9681\bigr] \)
24.1-a8	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 55 a - 111\) , \( -406 a + 717\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph