Elliptic curve isogeny class 3072.1-bx over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-bx
• Conductor: 3072.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3072.1-bx over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-bx contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3072.1-bx1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 96 a - 160\) , \( -632 a + 1096\bigr] \)
3072.1-bx2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 10\) , \( -8 a + 16\bigr] \)
3072.1-bx3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( -36 a + 60\bigr] \)
3072.1-bx4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32 a - 56\) , \( 142 a + 246\bigr] \)

Rank

Rank: \( 1 \)

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