Elliptic curve isogeny class 15.1-g over number field \(\Q(\sqrt{165}) \)

• Base field: \(\Q(\sqrt{165}) \)
• Label: 2.2.165.1-15.1-g
• Conductor: 15.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{165}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).

Elliptic curves in class 15.1-g over \(\Q(\sqrt{165}) \)

Isogeny class 15.1-g contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
15.1-g1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1438 a - 9852\) , \( -139212 a + 963920\bigr] \)
15.1-g2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8 a + 48\) , \( 48 a - 120\bigr] \)
15.1-g3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -447 a + 3198\) , \( -7386 a + 51344\bigr] \)
15.1-g4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 138 a - 852\) , \( -852 a + 6110\bigr] \)
15.1-g5	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 73 a - 402\) , \( 774 a - 5146\bigr] \)
15.1-g6	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1763 a - 12102\) , \( -100302 a + 694560\bigr] \)
15.1-g7	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1048 a - 7152\) , \( 46944 a - 324766\bigr] \)
15.1-g8	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 28088 a - 194352\) , \( -6474192 a + 44818500\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph