Elliptic curve isogeny class 392.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-392.1-b
• Conductor: 392.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 392.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 392.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
392.1-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a - 2\) , \( -100 a - 244\bigr] \)
392.1-b2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 202 a - 492\) , \( 2280 a - 5584\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph