Elliptic curve isogeny class 144.5-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-144.5-a
• Conductor: 144.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.5-a over \(\Q(\sqrt{17}) \)

Isogeny class 144.5-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
144.5-a1	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -1936 a - 3028\) , \( 64390 a + 100545\bigr] \)
144.5-a2	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 14 a + 22\) , \( 34 a + 53\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph