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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4608.1-f
• 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-f over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
4608.1-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9192 a - 15921\) , \( 631254 a - 1093364\bigr] \)
4608.1-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 627 a - 1086\) , \( 7953 a - 13775\bigr] \)
4608.1-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 36\) , \( -60 a + 100\bigr] \)
4608.1-f4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1668 a + 2889\) , \( 52704 a - 91286\bigr] \)

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