Elliptic curve isogeny class 119.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-119.1-b
• Conductor: 119.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 119.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 119.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
119.1-b1	\( \bigl[1\) , \( a\) , \( 0\) , \( 90 a - 204\) , \( 666 a - 1255\bigr] \)
119.1-b2	\( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
119.1-b3	\( \bigl[1\) , \( a\) , \( 0\) , \( 20 a - 39\) , \( -84 a + 122\bigr] \)
119.1-b4	\( \bigl[1\) , \( a\) , \( 0\) , \( -4\) , \( -4 a - 1\bigr] \)
119.1-b5	\( \bigl[1\) , \( a\) , \( 0\) , \( -20 a - 49\) , \( -100 a - 168\bigr] \)
119.1-b6	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -277 a + 354\) , \( 11005 a - 15638\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph