Elliptic curve isogeny class 612.1-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-612.1-a
• Conductor: 612.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 612.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 612.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
612.1-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \)
612.1-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
612.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 88 a - 226\) , \( -638 a + 1634\bigr] \)
612.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -88 a - 138\) , \( 638 a + 996\bigr] \)

Rank

Rank: \( 1 \)

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