Elliptic curve isogeny class 475.2-a over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-475.2-a
• Conductor: 475.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 475.2-a over \(\Q(\sqrt{17}) \)

Isogeny class 475.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
475.2-a1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 24 a - 59\) , \( 55 a - 144\bigr] \)
475.2-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -4 a - 8\) , \( -2 a - 7\bigr] \)
475.2-a3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 7 a - 15\) , \( 21 a - 54\bigr] \)
475.2-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -54 a - 133\) , \( -327 a - 677\bigr] \)

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