Elliptic curve isogeny class 26.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-26.1-a
• Conductor: 26.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 26.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 26.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
26.1-a1	\( \bigl[1\) , \( -a\) , \( 1\) , \( 13 a - 32\) , \( -28 a + 71\bigr] \)
26.1-a2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
26.1-a3	\( \bigl[1\) , \( -a\) , \( 1\) , \( -17 a - 26\) , \( 66 a + 103\bigr] \)
26.1-a4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4 a - 4\) , \( -13 a - 21\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph