Elliptic curve isogeny class 400.2-e over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-400.2-e
• Conductor: 400.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 400.2-e over \(\Q(\sqrt{6}) \)

Isogeny class 400.2-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
400.2-e1	\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 4 a + 9\bigr] \)
400.2-e2	\( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -50 a + 123\bigr] \)
400.2-e3	\( \bigl[a\) , \( a\) , \( 0\) , \( 31 a - 71\) , \( 129 a - 314\bigr] \)
400.2-e4	\( \bigl[a\) , \( a\) , \( a\) , \( -4 a - 14\) , \( -17 a - 42\bigr] \)

Rank

Rank: \( 0 \)

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