Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-6912.3-c
Conductor 6912.3
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 6912.3-c over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.3-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
6912.3-c1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 18\) , \( -26 a - 14\bigr] \)
6912.3-c2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 7\) , \( -7 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph