Elliptic curve isogeny class 81.1-c over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-81.1-c
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-c over \(\Q(\sqrt{17}) \)

Isogeny class 81.1-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
81.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 435 a - 1115\) , \( -7202 a + 18448\bigr] \)
81.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 285 a - 725\) , \( 3676 a - 9366\bigr] \)
81.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 525 a + 820\) , \( -10064 a - 15716\bigr] \)
81.1-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 195 a - 500\) , \( 1442 a - 3694\bigr] \)
81.1-c5	\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 50\) , \( 58 a - 132\bigr] \)
81.1-c6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 35\) , \( -58 a - 74\bigr] \)
81.1-c7	\( \bigl[1\) , \( -1\) , \( 1\) , \( -435 a - 680\) , \( 7202 a + 11246\bigr] \)
81.1-c8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -285 a - 440\) , \( -3676 a - 5690\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph