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

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

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

Curve label	Weierstrass Coefficients
4608.1-z1	\( \bigl[0\) , \( a\) , \( 0\) , \( -38 a - 75\) , \( -503 a - 898\bigr] \)
4608.1-z2	\( \bigl[0\) , \( a\) , \( 0\) , \( 12720 a - 22032\) , \( 1020420 a - 1767420\bigr] \)
4608.1-z3	\( \bigl[0\) , \( a\) , \( 0\) , \( 795 a - 1377\) , \( 15588 a - 27000\bigr] \)
4608.1-z4	\( \bigl[0\) , \( a\) , \( 0\) , \( 1020 a - 1782\) , \( 5436 a - 9450\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph