Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-114.4-a
Conductor 114.4
Rank \( 0 \)

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 114.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 114.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
114.4-a1 \( \bigl[1\) , \( a\) , \( a\) , \( 10\) , \( -6 a + 2\bigr] \)
114.4-a2 \( \bigl[1\) , \( a\) , \( a\) , \( -5 a + 10\) , \( -7 a + 24\bigr] \)
114.4-a3 \( \bigl[1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \)
114.4-a4 \( \bigl[1\) , \( a\) , \( a\) , \( 5 a + 170\) , \( -549 a + 68\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph