Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-114.1-a
Conductor 114.1
Rank \( 0 \)

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

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

Elliptic curves in class 114.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 114.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
114.1-a1 \( \bigl[1\) , \( -a\) , \( a\) , \( -a + 10\) , \( 6 a + 2\bigr] \)
114.1-a2 \( \bigl[1\) , \( -a\) , \( a\) , \( 4 a + 10\) , \( 7 a + 24\bigr] \)
114.1-a3 \( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \)
114.1-a4 \( \bigl[1\) , \( -a\) , \( a\) , \( -6 a + 170\) , \( 549 a + 68\bigr] \)

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