Elliptic curve isogeny class 392.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-392.1-b
• Conductor: 392.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{2}) \)

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

Elliptic curves in class 392.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 392.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
392.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
392.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( 90 a - 95\) , \( 458 a - 737\bigr] \)
392.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -25\bigr] \)
392.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( 1\bigr] \)
392.1-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( -90 a - 95\) , \( -458 a - 737\bigr] \)
392.1-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( 211\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph