Elliptic curve isogeny class 1176.1-p over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1176.1-p
• Conductor: 1176.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1176.1-p over \(\Q(\sqrt{3}) \)

Isogeny class 1176.1-p contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1176.1-p1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
1176.1-p2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 393 a - 685\) , \( 820 a - 1427\bigr] \)
1176.1-p3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 253 a - 440\) , \( -2785 a + 4824\bigr] \)
1176.1-p4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4033 a - 7055\) , \( -183280 a + 317619\bigr] \)

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