Elliptic curve isogeny class 676.1-b over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-676.1-b
• Conductor: 676.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.1-b over \(\Q(\sqrt{17}) \)

Isogeny class 676.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
676.1-b1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 343 a + 530\) , \( -24564 a - 38363\bigr] \)
676.1-b2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 7 a - 17\) , \( -21 a + 53\bigr] \)
676.1-b3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -77 a - 120\) , \( 326 a + 509\bigr] \)
676.1-b4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -397 a - 620\) , \( -6334 a - 9891\bigr] \)
676.1-b5	\( \bigl[1\) , \( -a\) , \( a\) , \( -8 a - 9\) , \( 20 a + 33\bigr] \)
676.1-b6	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -342 a + 872\) , \( 24905 a - 63799\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph