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

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

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

Curve label	Weierstrass Coefficients
10.1-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -24 a + 110\) , \( 250 a - 960\bigr] \)
10.1-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 30\) , \( 42 a - 128\bigr] \)
10.1-c3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 196 a - 730\) , \( 2746 a - 10608\bigr] \)
10.1-c4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 176 a - 890\) , \( 2490 a - 8960\bigr] \)

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