Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-162.1-b
Conductor 162.1
Rank \( 0 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 162.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 162.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
162.1-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -60588 a + 160290\) , \( 11487731 a - 30393691\bigr] \)
162.1-b2 \( \bigl[a\) , \( -1\) , \( 0\) , \( 153 a + 405\) , \( -35698 a - 94448\bigr] \)
162.1-b3 \( \bigl[a\) , \( -1\) , \( 0\) , \( 60588 a + 160290\) , \( 11487731 a + 30393691\bigr] \)
162.1-b4 \( \bigl[a\) , \( -1\) , \( 0\) , \( -20457 a - 54135\) , \( 1643612 a + 4348600\bigr] \)
162.1-b5 \( \bigl[a\) , \( -1\) , \( 0\) , \( -8487 a - 22455\) , \( -675418 a - 1786988\bigr] \)
162.1-b6 \( \bigl[a\) , \( -1\) , \( 0\) , \( -293022 a - 775440\) , \( 140361053 a + 371361301\bigr] \)
162.1-b7 \( \bigl[1\) , \( -1\) , \( 0\) , \( 20457 a - 54135\) , \( 1643612 a - 4348600\bigr] \)
162.1-b8 \( \bigl[1\) , \( -1\) , \( 0\) , \( 293022 a - 775440\) , \( 140361053 a - 371361301\bigr] \)