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

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

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

Curve label	Weierstrass Coefficients
60.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -160 a + 620\) , \( -2992 a + 11588\bigr] \)
60.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1100 a - 4260\) , \( -29760 a + 115260\bigr] \)
60.1-a3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 83300 a - 322620\) , \( -25726800 a + 99639468\bigr] \)
60.1-a4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 5200 a - 20140\) , \( -401680 a + 1555700\bigr] \)

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