Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-16128.5-n
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-n over \(\Q(\sqrt{-7}) \)

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

Curve label Weierstrass Coefficients
16128.5-n1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 33 a - 166\) , \( 234 a - 744\bigr] \)
16128.5-n2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -460\bigr] \)
16128.5-n3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -31 a - 134\) , \( -266 a - 644\bigr] \)
16128.5-n4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 6176\) , \( -69388\bigr] \)
16128.5-n5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1664\) , \( -9804\bigr] \)
16128.5-n6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -14624\) , \( 669300\bigr] \)
16128.5-n7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1344\) , \( -19404\bigr] \)
16128.5-n8 \( \bigl[0\) , \( 1\) , \( 0\) , \( -21504\) , \( -1220940\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph