Elliptic curve isogeny class 63.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-63.1-a
• Conductor: 63.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 63.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 63.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
63.1-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 1\) , \( -a - 2\bigr] \)
63.1-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -26 a - 29\) , \( 40 a + 64\bigr] \)
63.1-a3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -11 a - 14\) , \( -20 a - 29\bigr] \)
63.1-a4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -156 a - 239\) , \( -1336 a - 1870\bigr] \)

Rank

Rank: \( 0 \)

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