Elliptic curve isogeny class 15.1-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-15.1-a
• Conductor: 15.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 15.1-a over \(\Q(\sqrt{15}) \)

Isogeny class 15.1-a contains 10 curves linked by isogenies of degrees dividing 32.

Curve label	Weierstrass Coefficients
15.1-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( 155 a - 680\) , \( 2486 a - 10032\bigr] \)
15.1-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -110\) , \( 660\bigr] \)
15.1-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
15.1-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( 35\) , \( 98\bigr] \)
15.1-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( -10\) , \( -10\bigr] \)
15.1-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -12\bigr] \)
15.1-a7	\( \bigl[a\) , \( 1\) , \( a\) , \( -135\) , \( 390\bigr] \)
15.1-a8	\( \bigl[a\) , \( 1\) , \( a\) , \( -80\) , \( -402\bigr] \)
15.1-a9	\( \bigl[a\) , \( 1\) , \( a\) , \( -2160\) , \( 35220\bigr] \)
15.1-a10	\( \bigl[a\) , \( 1\) , \( a\) , \( -155 a - 680\) , \( -2486 a - 10032\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 32 & 8 & 16 & 8 & 4 & 16 & 2 & 32 & 4 \\ 32 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 & 32 \\ 8 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 & 8 \\ 16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 & 16 \\ 8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 & 8 \\ 4 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 & 4 \\ 16 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 & 16 \\ 2 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 & 2 \\ 32 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 & 32 \\ 4 & 32 & 8 & 16 & 8 & 4 & 16 & 2 & 32 & 1 \end{array}\right)\)

Isogeny graph