Elliptic curve isogeny class 363.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-363.1-b
• Conductor: 363.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 363.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 363.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
363.1-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -871 a + 2133\) , \( 6136 a - 15030\bigr] \)
363.1-b2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -230 a - 562\) , \( -1241 a - 3040\bigr] \)
363.1-b3	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -130 a - 317\) , \( 1086 a + 2660\bigr] \)
363.1-b4	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 2929 a - 7177\) , \( 138914 a - 340270\bigr] \)

Rank

Rank: \( 1 \)

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