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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1024.1-n
• 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-n over \(\Q(\sqrt{3}) \)

Isogeny class 1024.1-n contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1024.1-n1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 3\) , \( 4 a - 7\bigr] \)
1024.1-n2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 42 a - 73\) , \( 182 a - 315\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph