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

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

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

Curve label	Weierstrass Coefficients
4608.1-c1	\( \bigl[0\) , \( a\) , \( 0\) , \( 7348 a - 12726\) , \( -455468 a + 788894\bigr] \)
4608.1-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( 463 a - 801\) , \( -7196 a + 12464\bigr] \)
4608.1-c3	\( \bigl[0\) , \( a\) , \( 0\) , \( -152 a + 264\) , \( -23900 a + 41396\bigr] \)
4608.1-c4	\( \bigl[0\) , \( a\) , \( 0\) , \( -46 a - 99\) , \( 241 a + 406\bigr] \)

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