Elliptic curve isogeny class 900.2-i over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-900.2-i
• Conductor: 900.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 900.2-i over \(\Q(\sqrt{6}) \)

Isogeny class 900.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
900.2-i1	\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a + 54\) , \( 34 a - 71\bigr] \)
900.2-i2	\( \bigl[a\) , \( a\) , \( 0\) , \( -826 a - 2034\) , \( -6722 a - 16448\bigr] \)
900.2-i3	\( \bigl[a\) , \( a\) , \( 0\) , \( -481 a - 1179\) , \( 8320 a + 20380\bigr] \)
900.2-i4	\( \bigl[a\) , \( a\) , \( 0\) , \( -7696 a - 18864\) , \( 565450 a + 1385050\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph