Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-14112.3-b
Conductor 14112.3
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 14112.3-b over \(\Q(\sqrt{-2}) \)

Isogeny class 14112.3-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
14112.3-b1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 3 a - 6\) , \( 2 a - 6\bigr] \)
14112.3-b2 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 8 a - 26\) , \( -26 a + 34\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph