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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1734.1-e
• 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-e over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
1734.1-e1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \)
1734.1-e2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \)
1734.1-e3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \)
1734.1-e4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
1734.1-e5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
1734.1-e6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

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