Elliptic curve isogeny class 10.1-g over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-10.1-g
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-g over \(\Q(\sqrt{15}) \)

Isogeny class 10.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10.1-g1	\( \bigl[1\) , \( -a\) , \( 0\) , \( -404 a + 1569\) , \( -14780 a + 57241\bigr] \)
10.1-g2	\( \bigl[1\) , \( -a\) , \( 0\) , \( 186 a - 716\) , \( -2474 a + 9580\bigr] \)
10.1-g3	\( \bigl[1\) , \( -a\) , \( 0\) , \( 2981 a - 11541\) , \( -170271 a + 659455\bigr] \)
10.1-g4	\( \bigl[1\) , \( -a\) , \( 0\) , \( 3146 a - 12181\) , \( -149650 a + 579591\bigr] \)

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