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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.5-a
• 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-a over \(\Q(\sqrt{17}) \)

Isogeny class 676.5-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
676.5-a1	\( \bigl[1\) , \( a\) , \( a\) , \( 6 a - 88\) , \( 469 a + 1156\bigr] \)
676.5-a2	\( \bigl[1\) , \( a\) , \( a\) , \( a + 7\) , \( -20 a - 31\bigr] \)
676.5-a3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 52 a - 136\) , \( -143 a + 363\bigr] \)
676.5-a4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 3857 a - 9901\) , \( -184007 a + 471383\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph