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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-bu
• Conductor: 3072.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3072.1-bu1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -94 a + 163\) , \( -1183 a + 2049\bigr] \)
3072.1-bu2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( -32 a + 56\bigr] \)
3072.1-bu3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 204 a - 352\) , \( -2132 a + 3692\bigr] \)
3072.1-bu4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 64 a - 112\) , \( 328 a - 568\bigr] \)

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