Elliptic curve isogeny class 3600.1-m over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3600.1-m
• Conductor: 3600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3600.1-m over \(\Q(\sqrt{3}) \)

Isogeny class 3600.1-m contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
3600.1-m1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1526 a - 2643\) , \( -65251 a + 113018\bigr] \)
3600.1-m2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -154 a + 267\) , \( 1433 a - 2482\bigr] \)
3600.1-m3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 27\) , \( 41 a - 71\bigr] \)
3600.1-m4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 496 a - 867\) , \( -7687 a + 13309\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph