Elliptic curve isogeny class 64.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-64.1-a
• Conductor: 64.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 64.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 64.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
64.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 7\) , \( 0\bigr] \)
64.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a - 17\) , \( 17 a - 29\bigr] \)
64.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 10 a - 19\) , \( -36 a + 61\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph