Elliptic curve isogeny class 3136.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3136.1-c
• Conductor: 3136.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3136.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 3136.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3136.1-c1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a - 66\) , \( 131 a + 288\bigr] \)
3136.1-c2	\( \bigl[a\) , \( a\) , \( a\) , \( 24 a + 29\) , \( 100 a + 139\bigr] \)
3136.1-c3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -36 a - 52\) , \( 112 a + 158\bigr] \)
3136.1-c4	\( \bigl[a\) , \( -a\) , \( a\) , \( -24 a + 29\) , \( -100 a + 139\bigr] \)
3136.1-c5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -132 a - 196\) , \( 992 a + 1426\bigr] \)
3136.1-c6	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 15 a - 66\) , \( -131 a + 288\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph