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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-612.1-f
• Conductor: 612.1
• Rank: \( 0 \)

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

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

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

Isogeny class 612.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
612.1-f1	\( \bigl[1\) , \( a\) , \( 1\) , \( -92659 a - 144800\) , \( -22192717 a - 34655406\bigr] \)
612.1-f2	\( \bigl[1\) , \( a\) , \( 1\) , \( 2246 a + 3475\) , \( -152779 a - 238488\bigr] \)
612.1-f3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -57 a - 345\) , \( -1521 a + 585\bigr] \)
612.1-f4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -9762 a - 13020\) , \( -672588 a - 1114656\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph