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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-300.1-c
• 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-c over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
300.1-c1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -420 a - 1193\) , \( 7625 a + 19461\bigr] \)
300.1-c2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 30 a + 67\) , \( 83 a + 201\bigr] \)
300.1-c3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -5 a - 18\) , \( -6 a - 18\bigr] \)
300.1-c4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -90 a + 215\) , \( -1550 a + 3800\bigr] \)
300.1-c5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a - 25\) , \( 70 a - 172\bigr] \)
300.1-c6	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -80 a - 243\) , \( 609 a + 1377\bigr] \)
300.1-c7	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -455 a - 1128\) , \( 7614 a + 18660\bigr] \)
300.1-c8	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -7330 a - 18003\) , \( 523739 a + 1282785\bigr] \)

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