Elliptic curve isogeny class 900.1-f over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-f
• Conductor: 900.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 900.1-f over \(\Q(\sqrt{17}) \)

Isogeny class 900.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
900.1-f1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 187 a - 492\) , \( 1896 a - 4917\bigr] \)
900.1-f2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2558 a - 6553\) , \( 18714 a - 47939\bigr] \)
900.1-f3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 1918 a - 4913\) , \( 66066 a - 169235\bigr] \)
900.1-f4	\( \bigl[1\) , \( -a\) , \( a\) , \( -188 a - 304\) , \( -1897 a - 3020\bigr] \)

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