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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-b
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

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

Isogeny class 2304.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2304.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -312 a - 552\) , \( -13308 a - 23040\bigr] \)
2304.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 43288 a - 74976\) , \( 6476960 a - 11218424\bigr] \)
2304.1-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2758 a - 4776\) , \( 98288 a - 170240\bigr] \)
2304.1-b4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -9304 a + 16116\) , \( 2793284 a - 4838110\bigr] \)
2304.1-b5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 44 a - 84\) , \( -160 a + 272\bigr] \)
2304.1-b6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 96\) , \( -1312 a + 1712\bigr] \)

Rank

Rank: \( 0 \)

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