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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3600.1-c
• Conductor: 3600.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3600.1-c1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a + 10\) , \( -8 a - 1\bigr] \)
3600.1-c2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 5\) , \( -5 a - 1\bigr] \)
3600.1-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 42\) , \( 78 a + 135\bigr] \)
3600.1-c4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 80\) , \( -200 a - 1\bigr] \)

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