Elliptic curve isogeny class 588.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-588.1-a
• Conductor: 588.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 588.1-a over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
588.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \)
588.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
588.1-a3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -140 a - 346\) , \( -693 a - 1699\bigr] \)
588.1-a4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9140 a - 22396\) , \( -759825 a - 1861189\bigr] \)

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