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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.4-k
• Conductor: 676.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 676.4-k over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-k contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
676.4-k1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 881 a - 12698\) , \( -59247 a + 551857\bigr] \)
676.4-k2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9 a + 12\) , \( -15 a - 311\bigr] \)
676.4-k3	\( \bigl[1\) , \( -a\) , \( 0\) , \( -1996 a - 3119\) , \( -67668 a - 105671\bigr] \)
676.4-k4	\( \bigl[1\) , \( -a\) , \( 0\) , \( -407966 a - 638459\) , \( 204219854 a + 318919397\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 14 & 2 \\ 7 & 1 & 2 & 14 \\ 14 & 2 & 1 & 7 \\ 2 & 14 & 7 & 1 \end{array}\right)\)

Isogeny graph