Elliptic curve isogeny class 2401.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2401.1-b
• Conductor: 2401.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2401.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 2401.1-b contains 4 curves linked by isogenies of degrees dividing 35.

Curve label	Weierstrass Coefficients
2401.1-b1	\( \bigl[0\) , \( -1\) , \( 1\) , \( -14 \phi + 19\) , \( 21 \phi - 36\bigr] \)
2401.1-b2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -686 \phi + 915\) , \( -5831 \phi + 10420\bigr] \)
2401.1-b3	\( \bigl[0\) , \( -1\) , \( 1\) , \( 14 \phi + 5\) , \( -21 \phi - 15\bigr] \)
2401.1-b4	\( \bigl[0\) , \( 1\) , \( 1\) , \( 686 \phi + 229\) , \( 5831 \phi + 4589\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 35 & 5 & 7 \\ 35 & 1 & 7 & 5 \\ 5 & 7 & 1 & 35 \\ 7 & 5 & 35 & 1 \end{array}\right)\)

Isogeny graph