Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-16128.5-i
Conductor 16128.5
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 16128.5-i over \(\Q(\sqrt{-7}) \)

Isogeny class 16128.5-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
16128.5-i1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -544\) , \( 13888\bigr] \)
16128.5-i2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( 0\bigr] \)
16128.5-i3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \)
16128.5-i4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 26\) , \( -22 a + 88\bigr] \)
16128.5-i5 \( \bigl[0\) , \( -1\) , \( 0\) , \( -624\) , \( -5760\bigr] \)
16128.5-i6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a - 6\) , \( 54 a + 60\bigr] \)
16128.5-i7 \( \bigl[0\) , \( -1\) , \( 0\) , \( -784\) , \( 8704\bigr] \)
16128.5-i8 \( \bigl[0\) , \( -1\) , \( 0\) , \( -12544\) , \( 544960\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph