Elliptic curve isogeny class 144.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-144.1-a
• Conductor: 144.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 144.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
144.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -160 a - 238\) , \( 1458 a + 2072\bigr] \)
144.1-a2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2\) , \( -6 a - 8\bigr] \)
144.1-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a - 10\) , \( -14 a - 20\bigr] \)
144.1-a4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -648 a - 970\) , \( 10986 a + 15740\bigr] \)

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