Elliptic curve isogeny class 1024.1-q over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1024.1-q
• Conductor: 1024.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1024.1-q over \(\Q(\sqrt{3}) \)

Isogeny class 1024.1-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1024.1-q1	\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 11\) , \( -23 a + 38\bigr] \)
1024.1-q2	\( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -a\bigr] \)
1024.1-q3	\( \bigl[0\) , \( a\) , \( 0\) , \( -12 a - 20\) , \( 22 a + 38\bigr] \)
1024.1-q4	\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 11\) , \( -23 a - 38\bigr] \)

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