Elliptic curve isogeny class 600.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-600.1-b
• Conductor: 600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 600.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 600.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
600.1-b1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 149 a + 357\) , \( -606 a - 1488\bigr] \)
600.1-b2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -41 a - 103\) , \( -140 a - 344\bigr] \)
600.1-b3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -21 a - 53\) , \( 62 a + 150\bigr] \)
600.1-b4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -551 a - 1363\) , \( -11642 a - 28496\bigr] \)

Rank

Rank: \( 0 \)

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