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

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

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

Curve label	Weierstrass Coefficients
4608.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 102344 a - 177264\) , \( -23395972 a + 40523012\bigr] \)
4608.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6449 a - 11169\) , \( -356440 a + 617372\bigr] \)
4608.1-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -2116 a + 3666\) , \( -1248124 a + 2161814\bigr] \)
4608.1-b4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 78 a - 147\) , \( 399 a - 666\bigr] \)

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