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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.4-a
• 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-a over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
676.4-a1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 82\) , \( -470 a + 1625\bigr] \)
676.4-a2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 8\) , \( 19 a - 51\bigr] \)
676.4-a3	\( \bigl[1\) , \( a\) , \( a\) , \( -53 a - 83\) , \( 142 a + 221\bigr] \)
676.4-a4	\( \bigl[1\) , \( a\) , \( a\) , \( -3858 a - 6043\) , \( 184006 a + 287377\bigr] \)

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