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

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

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

Curve label	Weierstrass Coefficients
3072.1-bz1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 40 a - 56\) , \( 40 a - 72\bigr] \)
3072.1-bz2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 36\) , \( -72 a + 120\bigr] \)
3072.1-bz3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 320 a - 576\) , \( -4296 a + 7464\bigr] \)
3072.1-bz4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -4 a + 2\bigr] \)

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