Elliptic curve isogeny class 3600.1-n over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3600.1-n
• Conductor: 3600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3600.1-n over \(\Q(\sqrt{2}) \)

Isogeny class 3600.1-n contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3600.1-n1	\( \bigl[a\) , \( -1\) , \( a\) , \( 46 a + 31\) , \( -436 a - 685\bigr] \)
3600.1-n2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 10\) , \( 12 a - 15\bigr] \)
3600.1-n3	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 25 a - 35\) , \( 80 a - 116\bigr] \)
3600.1-n4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 10 a - 50\) , \( 50 a - 200\bigr] \)

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