Elliptic curve isogeny class 52.2-c over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-52.2-c
• Conductor: 52.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 52.2-c over \(\Q(\sqrt{17}) \)

Isogeny class 52.2-c contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
52.2-c1	\( \bigl[1\) , \( -a\) , \( a\) , \( -5999 a - 9401\) , \( -359412 a - 561343\bigr] \)
52.2-c2	\( \bigl[1\) , \( -a\) , \( a\) , \( 11 a + 19\) , \( 152 a + 237\bigr] \)
52.2-c3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 6 a - 18\) , \( -15 a + 35\bigr] \)
52.2-c4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 776 a - 4448\) , \( 27437 a - 120469\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 14 & 2 \\ 7 & 1 & 2 & 14 \\ 14 & 2 & 1 & 7 \\ 2 & 14 & 7 & 1 \end{array}\right)\)

Isogeny graph