Elliptic curve isogeny class 207.2-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-207.2-a
• Conductor: 207.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 207.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 207.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
207.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 29 a - 40\) , \( 86 a - 103\bigr] \)
207.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a\) , \( -1\bigr] \)
207.2-a3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a - 5\) , \( a\bigr] \)
207.2-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -31 a - 50\) , \( 100 a + 147\bigr] \)

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