Elliptic curve isogeny class 225.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-225.1-a
• Conductor: 225.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 225.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
225.1-a1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 12 a - 30\) , \( 44 a - 108\bigr] \)
225.1-a2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 37 a - 90\) , \( -129 a + 317\bigr] \)
225.1-a3	\( \bigl[a\) , \( 0\) , \( 1\) , \( -38 a - 90\) , \( 129 a + 317\bigr] \)
225.1-a4	\( \bigl[a\) , \( 0\) , \( 1\) , \( -13 a - 30\) , \( -44 a - 108\bigr] \)

Rank

Rank: \( 0 \)

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