Elliptic curve isogeny class 124.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-124.2-a
• Conductor: 124.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 124.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 124.2-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
124.2-a1	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( 35 \phi - 89\) , \( 204 \phi - 342\bigr] \)
124.2-a2	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
124.2-a3	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( -5 \phi - 9\) , \( -20 \phi - 22\bigr] \)
124.2-a4	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( 3305 \phi - 6949\) , \( 135572 \phi - 245838\bigr] \)
124.2-a5	\( \bigl[1\) , \( 1\) , \( 1\) , \( 8 \phi - 17\) , \( -6 \phi + 11\bigr] \)
124.2-a6	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( -465 \phi - 849\) , \( -9508 \phi - 11094\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 6 & 2 & 3 & 3 & 6 \\ 6 & 1 & 3 & 18 & 2 & 9 \\ 2 & 3 & 1 & 6 & 6 & 3 \\ 3 & 18 & 6 & 1 & 9 & 2 \\ 3 & 2 & 6 & 9 & 1 & 18 \\ 6 & 9 & 3 & 2 & 18 & 1 \end{array}\right)\)

Isogeny graph