Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-13122.5-b
Conductor 13122.5
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 13122.5-b over \(\Q(\sqrt{-2}) \)

Isogeny class 13122.5-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
13122.5-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \)
13122.5-b2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph