Elliptic curve isogeny class 576.4-g over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.4-g
• Conductor: 576.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.4-g over \(\Q(\sqrt{17}) \)

Isogeny class 576.4-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.4-g1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 8\) , \( -60 a + 152\bigr] \)
576.4-g2	\( \bigl[a\) , \( -a\) , \( 0\) , \( -4 a - 9\) , \( -3 a - 4\bigr] \)
576.4-g3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -34 a - 59\) , \( 175 a + 266\bigr] \)
576.4-g4	\( \bigl[a\) , \( -a\) , \( 0\) , \( -49 a - 144\) , \( -435 a - 508\bigr] \)

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