Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-19494.10-e
Conductor 19494.10
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 19494.10-e over \(\Q(\sqrt{-2}) \)

Isogeny class 19494.10-e contains 4 curves linked by isogenies of degrees dividing 27.

Curve label Weierstrass Coefficients
19494.10-e1 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -35 a - 8\) , \( -115 a + 97\bigr] \)
19494.10-e2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -17 a - 31\) , \( 29 a - 17\bigr] \)
19494.10-e3 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( 13 a + 628\) , \( 4122 a - 92\bigr] \)
19494.10-e4 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( 33 a + 83\) , \( -193 a + 257\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph