Elliptic curve isogeny class 2025.1-c over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2025.1-c
• Conductor: 2025.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 75 & 25 & 3 & 15 & 5 \\ 75 & 1 & 3 & 25 & 5 & 15 \\ 25 & 3 & 1 & 75 & 15 & 5 \\ 3 & 25 & 75 & 1 & 5 & 15 \\ 15 & 5 & 15 & 5 & 1 & 3 \\ 5 & 15 & 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 2025.1-c over \(\Q(\sqrt{5}) \)

Isogeny class 2025.1-c contains 6 curves linked by isogenies of degrees dividing 75.

Curve label	Weierstrass Coefficients
2025.1-c1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 \phi - 48\) , \( 109 \phi - 76\bigr] \)
2025.1-c2	\( \bigl[0\) , \( 0\) , \( 1\) , \( 54 \phi - 432\) , \( -2943 \phi + 2045\bigr] \)
2025.1-c3	\( \bigl[0\) , \( 0\) , \( 1\) , \( -6 \phi - 42\) , \( -109 \phi + 33\bigr] \)
2025.1-c4	\( \bigl[0\) , \( 0\) , \( 1\) , \( -54 \phi - 378\) , \( 2943 \phi - 898\bigr] \)
2025.1-c5	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 675 \phi + 506\bigr] \)
2025.1-c6	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -25 \phi - 19\bigr] \)