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

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

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

Curve label	Weierstrass Coefficients
60.1-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 406 a - 1575\) , \( -9175 a + 35535\bigr] \)
60.1-g2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 15\) , \( -15 a + 63\bigr] \)
60.1-g3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 26 a - 95\) , \( 105 a - 405\bigr] \)
60.1-g4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 386 a - 1655\) , \( -9087 a + 35763\bigr] \)

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