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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-k
• 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-k over \(\Q(\sqrt{3}) \)

Isogeny class 2304.1-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.1-k1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 204 a - 348\) , \( -540 a + 936\bigr] \)
2304.1-k2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 114 a - 198\) , \( 936 a - 1620\bigr] \)
2304.1-k3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1824 a - 3168\) , \( 56988 a - 98712\bigr] \)
2304.1-k4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a - 39\) , \( 95 a + 146\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph