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

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

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

Curve label	Weierstrass Coefficients
10.1-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
10.1-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 27 a - 111\) , \( 260 a - 1010\bigr] \)
10.1-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 477 a - 1861\) , \( 12680 a - 49110\bigr] \)
10.1-a4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 30 a - 116\bigr] \)

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