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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-120.1-l
• 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-l over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
120.1-l1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
120.1-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
120.1-l3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
120.1-l4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
120.1-l5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
120.1-l6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)

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