Elliptic curve isogeny class 20736.3-p over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20736.3-p
• Conductor: 20736.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 20736.3-p over \(\Q(\sqrt{-2}) \)

Isogeny class 20736.3-p contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
20736.3-p1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 198 a - 957\) , \( -3550 a + 11034\bigr] \)
20736.3-p2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -198 a - 957\) , \( -3550 a - 11034\bigr] \)
20736.3-p3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 12\) , \( 41 a + 9\bigr] \)
20736.3-p4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 12\) , \( 41 a - 9\bigr] \)
20736.3-p5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 57\) , \( -22 a - 198\bigr] \)
20736.3-p6	\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 57\) , \( -22 a + 198\bigr] \)
20736.3-p7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -162 a + 123\) , \( -526 a + 1458\bigr] \)
20736.3-p8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 162 a + 123\) , \( -526 a - 1458\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\ 12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\ 4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\ 12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\ 6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\ 2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\ 4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\ 3 & 4 & 12 & 4 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph