Elliptic curve isogeny class 676.4-j over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.4-j
• Conductor: 676.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.4-j over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-j contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
676.4-j1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 400 a - 1014\) , \( -2827 a + 7189\bigr] \)
676.4-j2	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -339 a - 609\) , \( -5167 a - 8283\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph