Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.2-b
Conductor 5202.2
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 5202.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.2-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
5202.2-b1 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 21 a + 23\) , \( 21 a - 77\bigr] \)
5202.2-b2 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 49 a - 8\) , \( -136 a - 148\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph