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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20736.3-l
• Conductor: 20736.3
• Rank: \( 1 \)

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

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

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

Isogeny class 20736.3-l contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
20736.3-l1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 717\) , \( -5522 a\bigr] \)
20736.3-l2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -990 a + 627\) , \( -11066 a + 30114\bigr] \)
20736.3-l3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 990 a + 627\) , \( -11066 a - 30114\bigr] \)
20736.3-l4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 22 a\bigr] \)
20736.3-l5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 33\) , \( -50 a\bigr] \)
20736.3-l6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 a - 93\) , \( 526 a + 126\bigr] \)
20736.3-l7	\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a - 93\) , \( 526 a - 126\bigr] \)
20736.3-l8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2913\) , \( 42790 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 5 & 10 & 10 & 10 & 2 \\ 2 & 1 & 4 & 10 & 20 & 20 & 5 & 4 \\ 2 & 4 & 1 & 10 & 20 & 5 & 20 & 4 \\ 5 & 10 & 10 & 1 & 2 & 2 & 2 & 10 \\ 10 & 20 & 20 & 2 & 1 & 4 & 4 & 5 \\ 10 & 20 & 5 & 2 & 4 & 1 & 4 & 20 \\ 10 & 5 & 20 & 2 & 4 & 4 & 1 & 20 \\ 2 & 4 & 4 & 10 & 5 & 20 & 20 & 1 \end{array}\right)\)

Isogeny graph