Elliptic curve isogeny class 441.3-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-441.3-a
• Conductor: 441.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.3-a over \(\Q(\sqrt{2}) \)

Isogeny class 441.3-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
441.3-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 119 a - 220\) , \( 1130 a - 1447\bigr] \)
441.3-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -a\) , \( -5 a + 5\bigr] \)
441.3-a3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5 a - 11\) , \( -10 a + 11\bigr] \)
441.3-a4	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 485 a - 891\) , \( 8995 a - 11639\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph