Elliptic curve isogeny class 882.1-f over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-882.1-f
• Conductor: 882.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 882.1-f over \(\Q(\sqrt{2}) \)

Isogeny class 882.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
882.1-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 2 a - 4\) , \( 4 a - 6\bigr] \)
882.1-f2	\( \bigl[1\) , \( -a\) , \( 1\) , \( -18 a - 27\) , \( 51 a + 72\bigr] \)
882.1-f3	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -3 a - 4\) , \( -213 a + 292\bigr] \)
882.1-f4	\( \bigl[1\) , \( -a\) , \( 1\) , \( -273 a - 417\) , \( 3189 a + 4560\bigr] \)

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