Elliptic curve isogeny class 3025.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3025.1-b
• Conductor: 3025.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3025.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 3025.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3025.1-b1	\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 430 \phi - 620\) , \( -310 \phi + 9655\bigr] \)
3025.1-b2	\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 5 \phi + 5\) , \( 0\bigr] \)
3025.1-b3	\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 21 \phi - 42\) , \( 39 \phi - 64\bigr] \)
3025.1-b4	\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -145 \phi - 145\) , \( 1040 \phi + 780\bigr] \)
3025.1-b5	\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -295 \phi - 295\) , \( -3800 \phi - 2850\bigr] \)
3025.1-b6	\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -429 \phi - 192\) , \( 739 \phi + 9536\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph