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

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

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

Curve label	Weierstrass Coefficients
3072.1-p1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 38 a - 65\) , \( -166 a + 285\bigr] \)
3072.1-p2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 9\) , \( 3 a + 3\bigr] \)
3072.1-p3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8 a - 15\) , \( 12 a - 21\bigr] \)
3072.1-p4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -22 a + 15\) , \( 78 a - 171\bigr] \)

Rank

Rank: \( 0 \)

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