Elliptic curve isogeny class 4900.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4900.1-a
• Conductor: 4900.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4900.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 4900.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4900.1-a1	\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 12 \phi + 12\) , \( 55 \phi + 41\bigr] \)
4900.1-a2	\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -88 \phi - 88\) , \( 375 \phi + 281\bigr] \)
4900.1-a3	\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -438 \phi - 438\) , \( -6345 \phi - 4759\bigr] \)
4900.1-a4	\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 1338 \phi - 2677\) , \( -33714 \phi + 59332\bigr] \)

Rank

Rank: \( 0 \)

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