Properties

Base field \(\Q(\sqrt{22}) \)
Label 2.2.88.1-144.1-m
Conductor 144.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 144.1-m over \(\Q(\sqrt{22}) \)

Isogeny class 144.1-m contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
144.1-m1 \( \bigl[0\) , \( a\) , \( 0\) , \( -786 a + 3694\) , \( -51420 a + 241185\bigr] \)
144.1-m2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -15 a - 83\) , \( -60 a - 286\bigr] \)
144.1-m3 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a - 58\) , \( -92 a - 437\bigr] \)
144.1-m4 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -205 a - 973\) , \( -4172 a - 19574\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph