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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-612.1-j
• 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-j over \(\Q(\sqrt{17}) \)

Isogeny class 612.1-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
612.1-j1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6007 a - 10823\) , \( -388147 a - 628623\bigr] \)
612.1-j2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 196 a - 505\) , \( -2004 a + 5129\bigr] \)
612.1-j3	\( \bigl[1\) , \( a\) , \( a\) , \( -34 a + 76\) , \( 219 a - 580\bigr] \)
612.1-j4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -397 a - 623\) , \( -6013 a - 9399\bigr] \)
612.1-j5	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6337 a - 9983\) , \( -393337 a - 614631\bigr] \)
612.1-j6	\( \bigl[1\) , \( 1\) , \( 1\) , \( 89804 a - 230134\) , \( 25887554 a - 66312741\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph