Elliptic curve isogeny class 576.6-m over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-576.6-m
• Conductor: 576.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.6-m over \(\Q(\sqrt{17}) \)

Isogeny class 576.6-m contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.6-m1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -32 a - 51\) , \( 1374 a + 2146\bigr] \)
576.6-m2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -7 a - 11\) , \( -23 a - 36\bigr] \)
576.6-m3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 71 a - 171\) , \( -344 a + 888\bigr] \)
576.6-m4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 416 a - 1056\) , \( 6133 a - 15705\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph