Elliptic curve isogeny class 2420.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2420.1-a
• Conductor: 2420.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2420.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 2420.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2420.1-a1	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( -14 \phi + 4\) , \( 150 \phi - 284\bigr] \)
2420.1-a2	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( \phi - 1\) , \( -6 \phi + 10\bigr] \)
2420.1-a3	\( \bigl[1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -8 \phi - 18\) , \( -17 \phi + 1\bigr] \)
2420.1-a4	\( \bigl[\phi + 1\) , \( 0\) , \( 1\) , \( 186 \phi - 596\) , \( 2230 \phi - 5724\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph