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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-bb
• 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-bb over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
3072.1-bb1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -94 a + 163\) , \( 1183 a - 2049\bigr] \)
3072.1-bb2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a - 22\) , \( 32 a - 56\bigr] \)
3072.1-bb3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 204 a - 352\) , \( 2132 a - 3692\bigr] \)
3072.1-bb4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 64 a - 112\) , \( -328 a + 568\bigr] \)

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