Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-90.1-f
Conductor 90.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 90.1-f over \(\Q(\sqrt{10}) \)

Isogeny class 90.1-f contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
90.1-f1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 12650 a - 45334\) , \( 1494440 a - 4876368\bigr] \)
90.1-f2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
90.1-f3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
90.1-f4 \( \bigl[1\) , \( 0\) , \( 1\) , \( 185 a - 469\) , \( 1934 a - 7134\bigr] \)
90.1-f5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
90.1-f6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
90.1-f7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
90.1-f8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
90.1-f9 \( \bigl[1\) , \( 0\) , \( 1\) , \( -185 a - 469\) , \( -1934 a - 7134\bigr] \)
90.1-f10 \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
90.1-f11 \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)
90.1-f12 \( \bigl[1\) , \( 0\) , \( 1\) , \( -12650 a - 45334\) , \( -1494440 a - 4876368\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 8 & 24 & 3 & 8 & 6 & 12 & 4 & 12 & 24 & 2 & 4 \\ 8 & 1 & 3 & 24 & 4 & 12 & 6 & 2 & 24 & 12 & 4 & 8 \\ 24 & 3 & 1 & 8 & 12 & 4 & 2 & 6 & 8 & 4 & 12 & 24 \\ 3 & 24 & 8 & 1 & 24 & 2 & 4 & 12 & 4 & 8 & 6 & 12 \\ 8 & 4 & 12 & 24 & 1 & 12 & 6 & 2 & 24 & 3 & 4 & 8 \\ 6 & 12 & 4 & 2 & 12 & 1 & 2 & 6 & 2 & 4 & 3 & 6 \\ 12 & 6 & 2 & 4 & 6 & 2 & 1 & 3 & 4 & 2 & 6 & 12 \\ 4 & 2 & 6 & 12 & 2 & 6 & 3 & 1 & 12 & 6 & 2 & 4 \\ 12 & 24 & 8 & 4 & 24 & 2 & 4 & 12 & 1 & 8 & 6 & 3 \\ 24 & 12 & 4 & 8 & 3 & 4 & 2 & 6 & 8 & 1 & 12 & 24 \\ 2 & 4 & 12 & 6 & 4 & 3 & 6 & 2 & 6 & 12 & 1 & 2 \\ 4 & 8 & 24 & 12 & 8 & 6 & 12 & 4 & 3 & 24 & 2 & 1 \end{array}\right)\)

Isogeny graph