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

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

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

Curve label	Weierstrass Coefficients
3072.1-bj1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 18\bigr] \)
3072.1-bj2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2272 a - 3936\) , \( -77040 a + 133440\bigr] \)
3072.1-bj3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 142 a - 246\) , \( -1176 a + 2040\bigr] \)
3072.1-bj4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 172 a - 336\) , \( -372 a + 780\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph