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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.5-l
• Conductor: 676.5
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
676.5-l1	\( \bigl[1\) , \( -a\) , \( a\) , \( -27 a + 69\) , \( -596 a + 1525\bigr] \)
676.5-l2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -34 a - 56\) , \( 133 a + 215\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph