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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-60.1-b
• Conductor: 60.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
60.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 406 a - 1575\) , \( 9175 a - 35535\bigr] \)
60.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 15\) , \( 15 a - 63\bigr] \)
60.1-b3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 26 a - 95\) , \( -105 a + 405\bigr] \)
60.1-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 386 a - 1655\) , \( 9087 a - 35763\bigr] \)

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