Elliptic curve isogeny class 64.5-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-64.5-a
• Conductor: 64.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 64.5-a over \(\Q(\sqrt{17}) \)

Isogeny class 64.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.5-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a + 2\) , \( 3 a - 4\bigr] \)
64.5-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -16 a - 25\) , \( -4 a - 9\bigr] \)
64.5-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -11 a - 15\) , \( -33 a - 51\bigr] \)
64.5-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -171 a - 265\) , \( -1835 a - 2865\bigr] \)

Rank

Rank: \( 0 \)

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