Elliptic curve isogeny class 49.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-49.1-a
• Conductor: 49.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 49.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 49.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 389 a - 919\) , \( 7231 a - 12956\bigr] \)
49.1-a2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 4 a - 9\) , \( 14 a - 27\bigr] \)
49.1-a3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
49.1-a4	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
49.1-a5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -5 a - 9\) , \( -14 a - 27\bigr] \)
49.1-a6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -390 a - 919\) , \( -7231 a - 12956\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 3 & 9 & 18 & 6 & 2 \\ 3 & 1 & 3 & 6 & 2 & 6 \\ 9 & 3 & 1 & 2 & 6 & 18 \\ 18 & 6 & 2 & 1 & 3 & 9 \\ 6 & 2 & 6 & 3 & 1 & 3 \\ 2 & 6 & 18 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph