Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-144.4-a
Conductor 144.4
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 144.4-a over \(\Q(\sqrt{17}) \)

Isogeny class 144.4-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
144.4-a1 \( \bigl[0\) , \( -a - 1\) , \( a\) , \( 1938 a - 4965\) , \( -66328 a + 169901\bigr] \)
144.4-a2 \( \bigl[0\) , \( -a - 1\) , \( a\) , \( -12 a + 35\) , \( -22 a + 53\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph