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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1024.1-r
• Conductor: 1024.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1024.1-r1	\( \bigl[0\) , \( a\) , \( 0\) , \( 118 a - 203\) , \( 849 a - 1470\bigr] \)
1024.1-r2	\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 13\) , \( 7 a - 12\bigr] \)
1024.1-r3	\( \bigl[0\) , \( a\) , \( 0\) , \( -2\) , \( -2 a\bigr] \)
1024.1-r4	\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a + 37\) , \( 89 a - 154\bigr] \)

Rank

Rank: \( 1 \)

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