Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-360.1-p
Conductor 360.1
Rank \( 0 \)

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 360.1-p over \(\Q(\sqrt{10}) \)

Isogeny class 360.1-p contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
360.1-p1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
360.1-p2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
360.1-p3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
360.1-p4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
360.1-p5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
360.1-p6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph