Elliptic curve isogeny class 120.1-b over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-120.1-b
• Conductor: 120.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 120.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 120.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
120.1-b1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -162 a - 616\) , \( 18578 a + 71960\bigr] \)
120.1-b2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 158 a + 624\) , \( -312 a - 1200\bigr] \)
120.1-b3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -42 a - 151\) , \( -82 a - 310\bigr] \)
120.1-b4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -402 a - 1546\) , \( 8270 a + 32036\bigr] \)
120.1-b5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -490 a - 1896\) , \( -12426 a - 48126\bigr] \)
120.1-b6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6402 a - 24796\) , \( 544370 a + 2108336\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph