Elliptic curve isogeny class 900.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-900.1-f
• Conductor: 900.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 900.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 900.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
900.1-f1	\( \bigl[0\) , \( a\) , \( 0\) , \( 30 a + 54\) , \( -18 a - 27\bigr] \)
900.1-f2	\( \bigl[a\) , \( a\) , \( 0\) , \( 1181 a - 2889\) , \( 34066 a - 83444\bigr] \)
900.1-f3	\( \bigl[a\) , \( a\) , \( 0\) , \( 656 a - 1614\) , \( 64906 a - 158984\bigr] \)
900.1-f4	\( \bigl[a\) , \( a\) , \( 0\) , \( 18866 a - 46224\) , \( 2202058 a - 5393966\bigr] \)

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