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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2025.1-d
• Conductor: 2025.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2025.1-d1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -180 \phi - 210\) , \( -2300 \phi - 1044\bigr] \)
2025.1-d2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -1620 \phi - 1890\) , \( 62100 \phi + 28181\bigr] \)
2025.1-d3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 180 \phi - 390\) , \( 2300 \phi - 3344\bigr] \)
2025.1-d4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 1620 \phi - 3510\) , \( -62100 \phi + 90281\bigr] \)
2025.1-d5	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -34\bigr] \)
2025.1-d6	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \)

Rank

Rank: \( 1 \)

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