Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-11979.2-a
Conductor 11979.2
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 11979.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 11979.2-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
11979.2-a1 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -62562 a + 242430\) , \( 30817677 a + 25165198\bigr] \)
11979.2-a2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -82 a + 320\) , \( 2607 a + 2038\bigr] \)
11979.2-a3 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2 a + 10\) , \( -23 a - 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph