Elliptic curve isogeny class 207.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-207.1-a
• Conductor: 207.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 207.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 207.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
207.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
207.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 30 a - 49\) , \( -150 a + 208\bigr] \)
207.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4\) , \( -6 a + 1\bigr] \)
207.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -30 a - 39\) , \( -126 a - 162\bigr] \)

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