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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-162.1-c
• Conductor: 162.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
162.1-c1	\( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -8\bigr] \)
162.1-c2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -435 a - 1683\) , \( 11742 a + 45477\bigr] \)
162.1-c3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 45 a + 177\) , \( -78 a - 303\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph