Elliptic curve isogeny class 81.1-b over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-81.1-b
• Conductor: 81.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 81.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 81.1-b contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
81.1-b1	\( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( -67\bigr] \)
81.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -960 a - 3720\) , \( 31878 a + 123464\bigr] \)
81.1-b3	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -4\bigr] \)
81.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 126 a + 488\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph