Elliptic curve isogeny class 162.1-f over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-162.1-f
• Conductor: 162.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 162.1-f over \(\Q(\sqrt{15}) \)

Isogeny class 162.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
162.1-f1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -100 a - 389\) , \( -1415 a - 5483\bigr] \)
162.1-f2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -6789 a - 26289\) , \( 786054 a + 3044376\bigr] \)
162.1-f3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 651 a + 2526\) , \( -11676 a - 45219\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph