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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-60.1-d
• 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-d over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
60.1-d1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a + 12\) , \( 12\bigr] \)
60.1-d2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 6 a - 8\) , \( -2 a + 18\bigr] \)
60.1-d3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 336 a - 1298\) , \( -6254 a + 24222\bigr] \)
60.1-d4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 21 a - 78\) , \( -82 a + 318\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph