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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-10.1-h
• 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-h over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
10.1-h1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a + 4\) , \( 4\bigr] \)
10.1-h2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 31 a - 111\) , \( -202 a + 788\bigr] \)
10.1-h3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 481 a - 1861\) , \( -11722 a + 45388\bigr] \)
10.1-h4	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 21\) , \( -22 a + 74\bigr] \)

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