Elliptic curve isogeny class 81.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-81.1-a
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 81.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 7152 a - 18327\) , \( -472886 a + 1211329\bigr] \)
81.1-a2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -48 a + 123\) , \( -134 a + 343\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph