Elliptic curve isogeny class 6534.12-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6534.12-c
• Conductor: 6534.12
• Rank: \( 0 \)

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

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

Elliptic curves in class 6534.12-c over \(\Q(\sqrt{-2}) \)

Isogeny class 6534.12-c contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
6534.12-c1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( a + 28\) , \( -59 a + 8\bigr] \)
6534.12-c2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -11 a + 19\) , \( 18 a - 3\bigr] \)
6534.12-c3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 248 a - 92\) , \( 1568 a + 1072\bigr] \)
6534.12-c4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 28 a - 37\) , \( -122 a + 59\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph