Elliptic curve isogeny class 10.1-f over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-10.1-f
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-f over \(\Q(\sqrt{15}) \)

Isogeny class 10.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10.1-f1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -23 a + 113\) , \( -230 a + 861\bigr] \)
10.1-f2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 17 a - 27\) , \( -42 a + 209\bigr] \)
10.1-f3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 197 a - 727\) , \( -2906 a + 11289\bigr] \)
10.1-f4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 177 a - 887\) , \( -2870 a + 8861\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph