Elliptic curve isogeny class 588.1-f over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-588.1-f
• Conductor: 588.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 588.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 588.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
588.1-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( a - 5\) , \( 5 a - 10\bigr] \)
588.1-f2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a - 14\) , \( 26 a + 45\bigr] \)