Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-13872.6-c
Conductor 13872.6
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 13872.6-c over \(\Q(\sqrt{-2}) \)

Isogeny class 13872.6-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
13872.6-c1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -6 a + 48\) , \( 140 a - 74\bigr] \)
13872.6-c2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 46 a - 44\) , \( -200 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph