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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1176.1-m
• 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-m over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
1176.1-m1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -52\bigr] \)
1176.1-m2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 391 a - 688\) , \( -428 a + 740\bigr] \)
1176.1-m3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 251 a - 443\) , \( 3037 a - 5266\bigr] \)
1176.1-m4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4031 a - 7058\) , \( 187312 a - 324676\bigr] \)

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