Elliptic curve isogeny class 10000.1-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-10000.1-e
• Conductor: 10000.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 10000.1-e over \(\Q(\sqrt{-2}) \)

Isogeny class 10000.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
10000.1-e1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 82\) , \( -572\bigr] \)
10000.1-e2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -43\) , \( -72\bigr] \)
10000.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( -125\bigr] \)
10000.1-e4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -668\) , \( -6322\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph