Elliptic curve isogeny class 1600.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1600.1-c
• Conductor: 1600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1600.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 1600.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1600.1-c1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a - 4\) , \( -a + 4\bigr] \)
1600.1-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12 a - 20\) , \( 44 a - 62\bigr] \)
1600.1-c3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8\) , \( 4 a + 2\bigr] \)
1600.1-c4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -12 a - 15\) , \( 34 a + 42\bigr] \)

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