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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1734.1-b
• Conductor: 1734.1
• Rank: \( 1 \)

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

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

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

Isogeny class 1734.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1734.1-b1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1644\) , \( 30942\bigr] \)
1734.1-b2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 226\) , \( 2232\bigr] \)
1734.1-b3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -114\) , \( 396\bigr] \)
1734.1-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -34\) , \( -68\bigr] \)
1734.1-b5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1734\) , \( 27936\bigr] \)
1734.1-b6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -27744\) , \( 1781010\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph