Elliptic curve isogeny class 147.1-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-147.1-a
• Conductor: 147.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 147.1-a over \(\Q(\sqrt{15}) \)

Isogeny class 147.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
147.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1090 a - 4212\) , \( 107190 a + 415152\bigr] \)
147.1-a2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a + 128\) , \( 62 a + 248\bigr] \)
147.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -130 a - 492\) , \( 246 a + 960\bigr] \)
147.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1250 a - 4832\) , \( -47858 a - 185352\bigr] \)
147.1-a5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1570 a - 6072\) , \( 65406 a + 253320\bigr] \)
147.1-a6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -25090 a - 97212\) , \( 4241382 a + 16426848\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph