Elliptic curve isogeny class 676.1-j over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.1-j
• Conductor: 676.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.1-j over \(\Q(\sqrt{17}) \)

Isogeny class 676.1-j contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
676.1-j1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \)
676.1-j2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \)
676.1-j3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph