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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-81.1-a
• 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-a over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -960 a - 3720\) , \( -31878 a - 123464\bigr] \)
81.1-a2	\( \bigl[0\) , \( 0\) , \( a\) , \( -14880 a - 57630\) , \( 1944558 a + 7531237\bigr] \)
81.1-a3	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 7686 a + 29764\bigr] \)
81.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -126 a - 488\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph