Elliptic curve isogeny class 450.2-l over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-450.2-l
• Conductor: 450.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 450.2-l over \(\Q(\sqrt{6}) \)

Isogeny class 450.2-l contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
450.2-l1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 10427 a - 25568\) , \( -900947 a + 2206823\bigr] \)
450.2-l2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 62 a - 158\) , \( -2465 a + 6035\bigr] \)
450.2-l3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -568 a + 1387\) , \( 65545 a - 160555\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph