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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-162.1-e
• 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-e over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
162.1-e1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -99 a - 381\) , \( 822 a + 3183\bigr] \)
162.1-e2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6789 a - 26294\) , \( -792843 a - 3070668\bigr] \)
162.1-e3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 651 a + 2521\) , \( 12327 a + 47742\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph