Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5625.2-b
Conductor 5625.2
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 5625.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 5625.2-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
5625.2-b1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \)
5625.2-b2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)
5625.2-b3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \)
5625.2-b4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \)
5625.2-b5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \)
5625.2-b6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \)
5625.2-b7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \)
5625.2-b8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph