Elliptic curve isogeny class 100.2-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-100.2-b
• Conductor: 100.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.2-b over \(\Q(\sqrt{6}) \)

Isogeny class 100.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.2-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 50 a - 123\bigr] \)
100.2-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -4 a - 9\bigr] \)
100.2-b3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -6 a - 11\) , \( 12 a + 29\bigr] \)
100.2-b4	\( \bigl[a\) , \( -a\) , \( a\) , \( 29 a - 74\) , \( -99 a + 241\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph