Elliptic curve isogeny class 100.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-100.1-b
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -7\) , \( 9\bigr] \)
100.1-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)
100.1-b3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -26 a - 63\) , \( -111 a - 272\bigr] \)
100.1-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -826 a - 2023\) , \( 19297 a + 47268\bigr] \)

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