Elliptic curve isogeny class 1922.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1922.1-a
• Conductor: 1922.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1922.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 1922.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1922.1-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 103 a - 226\) , \( 458 a - 873\bigr] \)
1922.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 25 a + 32\) , \( -128 a - 173\bigr] \)
1922.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -175 a - 328\) , \( -1808 a - 2205\bigr] \)
1922.1-a4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 533 a - 2056\) , \( -25762 a + 19263\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph