Elliptic curve isogeny class 300.3-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-300.3-a
• Conductor: 300.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 300.3-a over \(\Q(\sqrt{6}) \)

Isogeny class 300.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
300.3-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 1\) , \( 4 a + 2\bigr] \)
300.3-a2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -933 a - 2286\) , \( -21596 a - 52899\bigr] \)
300.3-a3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 82 a - 201\) , \( -327 a + 801\bigr] \)
300.3-a4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -223 a + 544\) , \( -3430 a + 8403\bigr] \)

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