Elliptic curve isogeny class 450.3-x over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-450.3-x
• Conductor: 450.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 450.3-x over \(\Q(\sqrt{6}) \)

Isogeny class 450.3-x contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
450.3-x1	\( \bigl[1\) , \( -1\) , \( a\) , \( -458 a - 1122\) , \( -8244 a - 20194\bigr] \)
450.3-x2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 36 a - 87\) , \( 171 a - 425\bigr] \)
450.3-x3	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 556 a - 1407\) , \( 11323 a - 27857\bigr] \)
450.3-x4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 6960 a - 17052\) , \( 293898 a - 719902\bigr] \)

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