Elliptic curve isogeny class 116.2-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-116.2-b
• Conductor: 116.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{5}) \)

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

Elliptic curves in class 116.2-b over \(\Q(\sqrt{5}) \)

Isogeny class 116.2-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
116.2-b1	\( \bigl[1\) , \( -\phi\) , \( \phi\) , \( -489 \phi - 588\) , \( -7663 \phi - 6684\bigr] \)
116.2-b2	\( \bigl[1\) , \( -\phi\) , \( \phi\) , \( \phi + 2\) , \( -\phi\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph