Elliptic curve isogeny class 1734.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1734.1-c
• Conductor: 1734.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1734.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 1734.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1734.1-c1	\( \bigl[a\) , \( -1\) , \( a\) , \( -217\) , \( -2063\bigr] \)
1734.1-c2	\( \bigl[a\) , \( -1\) , \( a\) , \( 1808\) , \( 37789\bigr] \)
1734.1-c3	\( \bigl[a\) , \( -1\) , \( a\) , \( -752\) , \( 6045\bigr] \)
1734.1-c4	\( \bigl[a\) , \( -1\) , \( a\) , \( -257\) , \( -1551\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph