Elliptic curve isogeny class 1936.3-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1936.3-a
• Conductor: 1936.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1936.3-a over \(\Q(\sqrt{5}) \)

Isogeny class 1936.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1936.3-a1	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -45 \phi - 193\) , \( 2368 \phi + 667\bigr] \)
1936.3-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 9 \phi - 10\) , \( -9\bigr] \)
1936.3-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41 \phi + 25\) , \( 19 \phi - 107\bigr] \)
1936.3-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 119 \phi - 1055\) , \( 10923 \phi - 7643\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph