Elliptic curve isogeny class 300.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-300.1-a
• Conductor: 300.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 300.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 300.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
300.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 3220 a - 7908\) , \( 158670 a - 388722\bigr] \)
300.1-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 70 a - 168\) , \( -90 a + 222\bigr] \)
300.1-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 55 a - 133\) , \( -302 a + 740\bigr] \)
300.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -116 a - 279\) , \( -1157 a - 2844\bigr] \)
300.1-a5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -16 a - 39\) , \( 39 a + 96\bigr] \)
300.1-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 880 a - 2158\) , \( -21542 a + 52760\bigr] \)
300.1-a7	\( \bigl[a\) , \( 1\) , \( 0\) , \( 205 a - 523\) , \( 2392 a - 5920\bigr] \)
300.1-a8	\( \bigl[a\) , \( 1\) , \( 0\) , \( 830 a - 2398\) , \( -20858 a + 48080\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 3 & 12 & 2 & 4 \\ 12 & 4 & 2 & 3 & 1 & 4 & 6 & 12 \\ 12 & 4 & 2 & 12 & 4 & 1 & 6 & 3 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 12 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph