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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-882.1-g
• 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-g over \(\Q(\sqrt{2}) \)

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

Curve label	Weierstrass Coefficients
882.1-g1	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 2 a - 4\) , \( 213 a + 292\bigr] \)
882.1-g2	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -3 a - 4\) , \( -4 a - 6\bigr] \)
882.1-g3	\( \bigl[1\) , \( a\) , \( 1\) , \( 18 a - 27\) , \( -51 a + 72\bigr] \)
882.1-g4	\( \bigl[1\) , \( a\) , \( 1\) , \( 273 a - 417\) , \( -3189 a + 4560\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph