Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-23409.8-e
Conductor 23409.8
Rank \( 1 \)

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 23409.8-e over \(\Q(\sqrt{-2}) \)

Isogeny class 23409.8-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
23409.8-e1 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -9785 a + 826\) , \( -286787 a + 492222\bigr] \)
23409.8-e2 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -605 a + 61\) , \( -4808 a + 8130\bigr] \)
23409.8-e3 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a - 1424\) , \( -1541 a + 43554\bigr] \)
23409.8-e4 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a + 106\) , \( -335 a - 384\bigr] \)

Rank

Rank: \( 1 \)

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