Elliptic curve isogeny class 10.2-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-10.2-a
• Conductor: 10.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.2-a over \(\Q(\sqrt{6}) \)

Isogeny class 10.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
10.2-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 166 a - 413\) , \( -1827 a + 4480\bigr] \)
10.2-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -5 a + 12\bigr] \)
10.2-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 133 a - 326\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph