Elliptic curve isogeny class 784.5-d over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-784.5-d
• Conductor: 784.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 784.5-d over \(\Q(\sqrt{17}) \)

Isogeny class 784.5-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
784.5-d1	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -54 a - 90\) , \( 539 a + 832\bigr] \)
784.5-d2	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 6 a + 10\) , \( -16 a - 25\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph