Elliptic curve isogeny class 1296.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1296.1-c
• Conductor: 1296.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1296.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 1296.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1296.1-c1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -36\) , \( -72 a\bigr] \)
1296.1-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -18\) , \( 26 a\bigr] \)
1296.1-c3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a + 16\) , \( -2 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph