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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-e
• Conductor: 900.1
• Rank: \( 1 \)

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

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

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

Isogeny class 900.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
900.1-e1	\( \bigl[1\) , \( -a\) , \( 1\) , \( 21 a - 52\) , \( -59 a + 150\bigr] \)
900.1-e2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4 a - 6\) , \( -8 a - 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph