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

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

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

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

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

Isogeny class 588.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
588.1-h1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \)
588.1-h2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
588.1-h3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 27 a - 51\) , \( 52 a - 92\bigr] \)
588.1-h4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1827 a - 3201\) , \( 57562 a - 99776\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph