Elliptic curve isogeny class 2304.1-q over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-q
• Conductor: 2304.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2304.1-q over \(\Q(\sqrt{3}) \)

Isogeny class 2304.1-q contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2304.1-q1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 172928 a - 299520\) , \( 51615872 a - 89401312\bigr] \)
2304.1-q2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 48\) , \( -540 a\bigr] \)
2304.1-q3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -21728 a + 37635\) , \( 2826656 a - 4895912\bigr] \)
2304.1-q4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 728 a - 1260\) , \( 10928 a - 18928\bigr] \)
2304.1-q5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -72\) , \( -108 a\bigr] \)
2304.1-q6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 10808 a - 18720\) , \( 811136 a - 1404928\bigr] \)
2304.1-q7	\( \bigl[0\) , \( -a\) , \( 0\) , \( -1152\) , \( -8316 a\bigr] \)
2304.1-q8	\( \bigl[0\) , \( -a\) , \( 0\) , \( 9968 a - 17280\) , \( 940352 a - 1628704\bigr] \)

Rank

Rank: \( 1 \)

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