Elliptic curve isogeny class 3249.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3249.1-b
• Conductor: 3249.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3249.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 3249.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3249.1-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
3249.1-b2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \)
3249.1-b3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \)
3249.1-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \)

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