Elliptic curve isogeny class 20808.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20808.4-a
• Conductor: 20808.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 20808.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 20808.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
20808.4-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( -1566 a - 615\) , \( 27618 a - 15789\bigr] \)
20808.4-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -546 a + 745\) , \( 3582 a + 13091\bigr] \)
20808.4-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( -96 a - 15\) , \( 528 a - 93\bigr] \)
20808.4-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( 24 a - 25\) , \( 72 a - 55\bigr] \)

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