Elliptic curve isogeny class 3380.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3380.1-a
• Conductor: 3380.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3380.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 3380.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3380.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -67\) , \( -441\bigr] \)
3380.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -7\) , \( -1\bigr] \)
3380.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -87\) , \( -289\bigr] \)
3380.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1387\) , \( -19529\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph