Elliptic curve isogeny class 10.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-10.1-b
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 10.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 117 a - 292\) , \( 1111 a - 2738\bigr] \)
10.1-b2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 2 a - 4\bigr] \)
10.1-b3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a + 23\) , \( -2 a + 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph