Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-144.1-c
Conductor 144.1
Rank \( 1 \)

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 144.1-c over \(\Q(\sqrt{10}) \)

Isogeny class 144.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
144.1-c1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \)
144.1-c2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
144.1-c3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \)
144.1-c4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -24\) , \( 36\bigr] \)
144.1-c5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)
144.1-c6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \)

Rank

Rank: \( 1 \)

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