Elliptic curve isogeny class 60.1-f over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-60.1-f
• Conductor: 60.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 60.1-f over \(\Q(\sqrt{15}) \)

Isogeny class 60.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
60.1-f1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6306 a - 24396\) , \( -537620 a + 2082234\bigr] \)
60.1-f2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 86 a - 306\) , \( -668 a + 2628\bigr] \)
60.1-f3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 401 a - 1526\) , \( 7780 a - 30091\bigr] \)
60.1-f4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6311 a - 24416\) , \( -536714 a + 2078723\bigr] \)

Rank

Rank: \( 1 \)

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