Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-22050.2-e
Conductor 22050.2
Rank not recorded

Related objects

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

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

Elliptic curves in class 22050.2-e over \(\Q(\sqrt{-2}) \)

Isogeny class 22050.2-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
22050.2-e1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -81\) , \( 6561\bigr] \)
22050.2-e2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 729\) , \( -176985\bigr] \)
22050.2-e3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -41\) , \( -39\bigr] \)
22050.2-e4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -6451\) , \( 124931\bigr] \)
22050.2-e5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -2701\) , \( -52819\bigr] \)
22050.2-e6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -361\) , \( 2585\bigr] \)
22050.2-e7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -2681\) , \( -53655\bigr] \)
22050.2-e8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -5761\) , \( 167825\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph