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

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

Isogeny class 676.4-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
676.4-e1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 2041 a - 5233\) , \( 161536 a - 413796\bigr] \)
676.4-e2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 175 a + 274\) , \( -2595 a - 4052\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph