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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4608.1-a
• Conductor: 4608.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
4608.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 660 a - 1143\) , \( 12144 a - 21034\bigr] \)
4608.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 78\) , \( 153 a - 265\bigr] \)
4608.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 36\) , \( -60 a - 100\bigr] \)
4608.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a + 207\) , \( 1014 a - 1756\bigr] \)

Rank

Rank: \( 0 \)

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