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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-81.1-b
• 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-b over \(\Q(\sqrt{17}) \)

Isogeny class 81.1-b contains 4 curves linked by isogenies of degrees dividing 51.

Curve label	Weierstrass Coefficients
81.1-b1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -6 a - 12\) , \( 14 a + 19\bigr] \)
81.1-b2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -54 a - 108\) , \( -378 a - 520\bigr] \)
81.1-b3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 a - 18\) , \( -14 a + 33\bigr] \)
81.1-b4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 54 a - 162\) , \( 378 a - 898\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 51 & 17 & 3 \\ 51 & 1 & 3 & 17 \\ 17 & 3 & 1 & 51 \\ 3 & 17 & 51 & 1 \end{array}\right)\)

Isogeny graph