Elliptic curve isogeny class 200.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-200.1-b
• Conductor: 200.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 200.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 200.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-b1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 4\) , \( 6\bigr] \)
200.1-b2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
200.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -40 a - 98\) , \( -198 a - 485\bigr] \)
200.1-b4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -26\) , \( 40\bigr] \)

Rank

Rank: \( 1 \)

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