Elliptic curve isogeny class 676.5-j over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.5-j
• Conductor: 676.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.5-j over \(\Q(\sqrt{17}) \)

Isogeny class 676.5-j contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
676.5-j1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -398 a - 614\) , \( 2428 a + 3748\bigr] \)
676.5-j2	\( \bigl[1\) , \( -a\) , \( 1\) , \( 339 a - 948\) , \( 5167 a - 13450\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph