Elliptic curve isogeny class 4608.1-bf over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4608.1-bf
• Conductor: 4608.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 4608.1-bf over \(\Q(\sqrt{3}) \)

Isogeny class 4608.1-bf contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4608.1-bf1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 7348 a - 12726\) , \( 455468 a - 788894\bigr] \)
4608.1-bf2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 463 a - 801\) , \( 7196 a - 12464\bigr] \)
4608.1-bf3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -152 a + 264\) , \( 23900 a - 41396\bigr] \)
4608.1-bf4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -46 a - 99\) , \( -241 a - 406\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph