Elliptic curve isogeny class 576.7-p over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.7-p
• Conductor: 576.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.7-p over \(\Q(\sqrt{17}) \)

Isogeny class 576.7-p contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.7-p1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 12 a + 15\) , \( -27 a - 45\bigr] \)
576.7-p2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -3 a - 5\) , \( -16 a - 25\bigr] \)
576.7-p3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -3 a + 8\) , \( 0\bigr] \)
576.7-p4	\( \bigl[a\) , \( -a\) , \( a\) , \( 20 a - 55\) , \( -60 a + 152\bigr] \)

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