Elliptic curve isogeny class 100.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-100.1-a
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 100.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 100.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
100.1-a1	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 24 \phi - 50\) , \( -104 \phi + 174\bigr] \)
100.1-a2	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -15 \phi - 15\) , \( -69 \phi - 48\bigr] \)
100.1-a3	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 0\) , \( 0\bigr] \)
100.1-a4	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( -111 \phi + 220\) , \( -287 \phi + 528\bigr] \)