Elliptic curve isogeny class 450.1-g over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-450.1-g
• Number of curves: 4
• Conductor: 450.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 450.1-g over \(\Q(\sqrt{6}) \)

Isogeny class 450.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
450.1-g1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4842 a + 11451\) , \( 67614 a + 162495\bigr] \)
450.1-g2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1218 a - 3009\) , \( 7290 a + 17811\bigr] \)
450.1-g3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -738 a - 1809\) , \( -17478 a - 42813\bigr] \)
450.1-g4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -14958 a - 36669\) , \( 1547478 a + 3790503\bigr] \)